Geometric realizations of curvature:
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are re...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
London
Imperial College Press
c2012
|
| Schriftenreihe: | ICP advanced texts in mathematics
v. 6 |
| Schlagwörter: | |
| Links: | http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc |
| Zusammenfassung: | A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature |
| Umfang: | ix, 252 p. ill |
| ISBN: | 9781848167421 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV044633496 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 171120s2012 xx a||| o|||| 00||| eng d | ||
| 020 | |a 9781848167421 |c electronic bk. |9 978-1-84816-742-1 | ||
| 024 | 7 | |a 10.1142/P787 |2 doi | |
| 035 | |a (ZDB-124-WOP)00002661 | ||
| 035 | |a (OCoLC)915306485 | ||
| 035 | |a (DE-599)BVBBV044633496 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-92 | ||
| 082 | 0 | |a 516 |2 22 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 100 | 1 | |a Brozos-Vazquez, Miguel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric realizations of curvature |c Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic |
| 264 | 1 | |a London |b Imperial College Press |c c2012 | |
| 300 | |a ix, 252 p. |b ill | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a ICP advanced texts in mathematics |v v. 6 | |
| 520 | |a A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature | ||
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Geometry, Affine | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | 1 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Gilkey, Peter B. |e Sonstige |4 oth | |
| 700 | 1 | |a Nikcevic, Stana |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 1848167415 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9781848167414 |
| 856 | 4 | 0 | |u http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc |x Verlag |z URL des Erstveroeffentlichers |3 Volltext |
| 912 | |a ZDB-124-WOP | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-030031468 | |
| 966 | e | |u http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc |l DE-92 |p ZDB-124-WOP |q FHN_PDA_WOP |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1818983717685690368 |
|---|---|
| any_adam_object | |
| author | Brozos-Vazquez, Miguel |
| author_facet | Brozos-Vazquez, Miguel |
| author_role | aut |
| author_sort | Brozos-Vazquez, Miguel |
| author_variant | m b v mbv |
| building | Verbundindex |
| bvnumber | BV044633496 |
| classification_rvk | SK 370 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00002661 (OCoLC)915306485 (DE-599)BVBBV044633496 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03725nam a2200505zcb4500</leader><controlfield tag="001">BV044633496</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">171120s2012 xx a||| o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848167421</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-1-84816-742-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1142/P787</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-124-WOP)00002661</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)915306485</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044633496</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brozos-Vazquez, Miguel</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric realizations of curvature</subfield><subfield code="c">Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Imperial College Press</subfield><subfield code="c">c2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">ix, 252 p.</subfield><subfield code="b">ill</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">ICP advanced texts in mathematics</subfield><subfield code="v">v. 6</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Affine</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannsche Geometrie</subfield><subfield code="0">(DE-588)4128462-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Riemannsche Geometrie</subfield><subfield code="0">(DE-588)4128462-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gilkey, Peter B.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nikcevic, Stana</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">1848167415</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9781848167414</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveroeffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-124-WOP</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030031468</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc</subfield><subfield code="l">DE-92</subfield><subfield code="p">ZDB-124-WOP</subfield><subfield code="q">FHN_PDA_WOP</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044633496 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:07:33Z |
| institution | BVB |
| isbn | 9781848167421 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030031468 |
| oclc_num | 915306485 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | ix, 252 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Imperial College Press |
| record_format | marc |
| series2 | ICP advanced texts in mathematics |
| spelling | Brozos-Vazquez, Miguel Verfasser aut Geometric realizations of curvature Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic London Imperial College Press c2012 ix, 252 p. ill txt rdacontent c rdamedia cr rdacarrier ICP advanced texts in mathematics v. 6 A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature Geometry Geometry, Affine Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Riemannsche Geometrie (DE-588)4128462-8 s 1\p DE-604 Gilkey, Peter B. Sonstige oth Nikcevic, Stana Sonstige oth Erscheint auch als Druck-Ausgabe 1848167415 Erscheint auch als Druck-Ausgabe 9781848167414 http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brozos-Vazquez, Miguel Geometric realizations of curvature Geometry Geometry, Affine Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4128462-8 |
| title | Geometric realizations of curvature |
| title_auth | Geometric realizations of curvature |
| title_exact_search | Geometric realizations of curvature |
| title_full | Geometric realizations of curvature Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic |
| title_fullStr | Geometric realizations of curvature Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic |
| title_full_unstemmed | Geometric realizations of curvature Miguel Brozos Vazquez, Peter B. Gilkey, Stana Nikcevic |
| title_short | Geometric realizations of curvature |
| title_sort | geometric realizations of curvature |
| topic | Geometry Geometry, Affine Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Geometry Geometry, Affine Differentialgeometrie Riemannsche Geometrie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc |
| work_keys_str_mv | AT brozosvazquezmiguel geometricrealizationsofcurvature AT gilkeypeterb geometricrealizationsofcurvature AT nikcevicstana geometricrealizationsofcurvature |