Conformal vector fields, Ricci solitons and related topics:
This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixe...
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore
Springer
[2024]
|
| Schriftenreihe: | Infosys Science Foundation series in mathematical sciences
Infosys Science Foundation Series |
| Schlagwörter: | |
| Zusammenfassung: | This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics |
| Beschreibung: | Preface; 1. Manifolds and Submanifolds Reviewed; 2. Lie Group and Lie Derivative; 3. Conformal Transformations; 4. Conformal Vector Fields; 5. Integral Formulas and Conformal Vector Fields; 6. Conformal Vector Fields on Lorentzian Manifolds; 7. Ricci Solitons; 8. Conformal Vector Fields and Ricci Solitons in Complex and Contact Geometries; 9. Quasi-Einstein Manifolds and Conformal Vector Fields |
| Umfang: | xi, 158 Seiten 430 gr |
| ISBN: | 9789819992577 |
Internformat
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| 100 | 1 | |a Sharma, Ramesh |e Verfasser |4 aut | |
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| 500 | |a Preface; 1. Manifolds and Submanifolds Reviewed; 2. Lie Group and Lie Derivative; 3. Conformal Transformations; 4. Conformal Vector Fields; 5. Integral Formulas and Conformal Vector Fields; 6. Conformal Vector Fields on Lorentzian Manifolds; 7. Ricci Solitons; 8. Conformal Vector Fields and Ricci Solitons in Complex and Contact Geometries; 9. Quasi-Einstein Manifolds and Conformal Vector Fields | ||
| 520 | |a This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics | ||
| 650 | 4 | |a bicssc | |
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| 650 | 4 | |a General relativity (Physics) | |
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Datensatz im Suchindex
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| author | Sharma, Ramesh Deshmukh, Sharief |
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| bvnumber | BV049567966 |
| ctrlnum | (OCoLC)1429572323 (DE-599)BVBBV049567966 |
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| id | DE-604.BV049567966 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T20:15:38Z |
| institution | BVB |
| isbn | 9789819992577 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034913221 |
| oclc_num | 1429572323 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xi, 158 Seiten 430 gr |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series2 | Infosys Science Foundation series in mathematical sciences Infosys Science Foundation Series |
| spelling | Sharma, Ramesh Verfasser aut Conformal vector fields, Ricci solitons and related topics Ramesh Sharma, Sharief Deshmukh Singapore Springer [2024] xi, 158 Seiten 430 gr txt rdacontent n rdamedia nc rdacarrier Infosys Science Foundation series in mathematical sciences Infosys Science Foundation Series Preface; 1. Manifolds and Submanifolds Reviewed; 2. Lie Group and Lie Derivative; 3. Conformal Transformations; 4. Conformal Vector Fields; 5. Integral Formulas and Conformal Vector Fields; 6. Conformal Vector Fields on Lorentzian Manifolds; 7. Ricci Solitons; 8. Conformal Vector Fields and Ricci Solitons in Complex and Contact Geometries; 9. Quasi-Einstein Manifolds and Conformal Vector Fields This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics bicssc bisacsh Manifolds (Mathematics) Geometry, Differential General relativity (Physics) Global analysis (Mathematics) Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Ricci-Fluss (DE-588)7531847-7 gnd rswk-swf Hardcover, Softcover / Mathematik/Analysis Pseudo-Riemannscher Raum (DE-588)4176163-7 s Ricci-Fluss (DE-588)7531847-7 s Soliton (DE-588)4135213-0 s DE-604 Deshmukh, Sharief Verfasser aut Erscheint auch als Online-Ausgabe 978-981-99-9258-4 |
| spellingShingle | Sharma, Ramesh Deshmukh, Sharief Conformal vector fields, Ricci solitons and related topics bicssc bisacsh Manifolds (Mathematics) Geometry, Differential General relativity (Physics) Global analysis (Mathematics) Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd Soliton (DE-588)4135213-0 gnd Ricci-Fluss (DE-588)7531847-7 gnd |
| subject_GND | (DE-588)4176163-7 (DE-588)4135213-0 (DE-588)7531847-7 |
| title | Conformal vector fields, Ricci solitons and related topics |
| title_auth | Conformal vector fields, Ricci solitons and related topics |
| title_exact_search | Conformal vector fields, Ricci solitons and related topics |
| title_full | Conformal vector fields, Ricci solitons and related topics Ramesh Sharma, Sharief Deshmukh |
| title_fullStr | Conformal vector fields, Ricci solitons and related topics Ramesh Sharma, Sharief Deshmukh |
| title_full_unstemmed | Conformal vector fields, Ricci solitons and related topics Ramesh Sharma, Sharief Deshmukh |
| title_short | Conformal vector fields, Ricci solitons and related topics |
| title_sort | conformal vector fields ricci solitons and related topics |
| topic | bicssc bisacsh Manifolds (Mathematics) Geometry, Differential General relativity (Physics) Global analysis (Mathematics) Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd Soliton (DE-588)4135213-0 gnd Ricci-Fluss (DE-588)7531847-7 gnd |
| topic_facet | bicssc bisacsh Manifolds (Mathematics) Geometry, Differential General relativity (Physics) Global analysis (Mathematics) Pseudo-Riemannscher Raum Soliton Ricci-Fluss |
| work_keys_str_mv | AT sharmaramesh conformalvectorfieldsriccisolitonsandrelatedtopics AT deshmukhsharief conformalvectorfieldsriccisolitonsandrelatedtopics |