Verfügbarkeit: Geometry of hypersurfaces | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Cecil, Thomas E. 1945- (VerfasserIn), Ryan, Patrick J. (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	Englisch
Veröffentlicht:	New York ; Heidelberg ; Dordrecht ; London Springer [2015]
Schriftenreihe:	Springer monographs in mathematics
Schlagwörter:	Mathematics Topological groups Lie groups Differential geometry Hyperbolic geometry Differential Geometry Topological Groups, Lie Groups Hyperbolic Geometry Mathematik
Links:	https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 https://doi.org/10.1007/978-1-4939-3246-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632857&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632857&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	1 Online Ressource (XI, 596 Seiten) Illustrationen, Diagramme
ISBN:	9781493932467
ISSN:	1439-7382
DOI:	10.1007/978-1-4939-3246-7

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Datensatz im Suchindex

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adam_text	GEOMETRY OF HYPERSURFACES / CECIL, THOMAS E. : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS PREFACE 1. INTRODUCTION 2. SUBMANIFOLDS OF REAL SPACE FORMS 3. ISOPARAMETRIC HYPERSURFACES 4. SUBMANIFOLDS IN LIE SPHERE GEOMETRY 5. DUPIN HYPERSURFACES 6. REAL HYPERSURFACES IN COMPLEX SPACE FORMS 7. COMPLEX SUBMANIFOLDS OF CPN AND CHN 8. HOPF HYPERSURFACES 9. HYPERSURFACES IN QUATERNIONIC SPACE FORMS APPENDIX A. SUMMARY OF NOTATION REFERENCES INDEX DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. GEOMETRY OF HYPERSURFACES / CECIL, THOMAS E. : 2015 ABSTRACT / INHALTSTEXT THIS EXPOSITION PROVIDES THE STATE-OF-THE ART ON THE DIFFERENTIAL GEOMETRY OF HYPERSURFACES IN REAL, COMPLEX, AND QUATERNIONIC SPACE FORMS. SPECIAL EMPHASIS IS PLACED ON ISOPARAMETRIC AND DUPIN HYPERSURFACES IN REAL SPACE FORMS AS WELL AS HOPF HYPERSURFACES IN COMPLEX SPACE FORMS. THE BOOK IS ACCESSIBLE TO A READER WHO HAS COMPLETED A ONE-YEAR GRADUATE COURSE IN DIFFERENTIAL GEOMETRY. THE TEXT, INCLUDING OPEN PROBLEMS AND AN EXTENSIVE LIST OF REFERENCES, IS AN EXCELLENT RESOURCE FOR RESEARCHERS IN THIS AREA. GEOMETRY OF HYPERSURFACES BEGINS WITH THE BASIC THEORY OF SUBMANIFOLDS IN REAL SPACE FORMS. TOPICS INCLUDE SHAPE OPERATORS, PRINCIPAL CURVATURES AND FOLIATIONS, TUBES AND PARALLEL HYPERSURFACES, CURVATURE SPHERES AND FOCAL SUBMANIFOLDS. THE FOCUS THEN TURNS TO THE THEORY OF ISOPARAMETRIC HYPERSURFACES IN SPHERES. IMPORTANT EXAMPLES AND CLASSIFICATION RESULTS ARE GIVEN, INCLUDING THE CONSTRUCTION OF ISOPARAMETRIC HYPERSURFACES BASED ON REPRESENTATIONS OF CLIFFORD ALGEBRAS. AN IN-DEPTH TREATMENT OF DUPIN HYPERSURFACES FOLLOWS WITH RESULTS THAT ARE PROVED IN THE CONTEXT OF LIE SPHERE GEOMETRY AS WELL AS THOSE THAT ARE OBTAINED USING STANDARD METHODS OF SUBMANIFOLD THEORY. NEXT COMES A THOROUGH TREATMENT OF THE THEORY OF REAL HYPERSURFACES IN COMPLEX SPACE FORMS. A CENTRAL FOCUS IS A COMPLETE PROOF OF THE CLASSIFICATION OF HOPF HYPERSURFACES WITH CONSTANT PRINCIPAL CURVATURES DUE TO KIMURA AND BERNDT. THE BOOK CONCLUDES WITH THE BASIC THEORY OF REAL HYPERSURFACES IN QUATERNIONIC SPACE FORMS, INCLUDING STATEMENTS OF THE MAJOR CLASSIFICATION RESULTS AND DIRECTIONS FOR FURTHER RESEARCH DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spellingShingle	Cecil, Thomas E. 1945- Ryan, Patrick J. Geometry of hypersurfaces Mathematics Topological groups Lie groups Differential geometry Hyperbolic geometry Differential Geometry Topological Groups, Lie Groups Hyperbolic Geometry Mathematik
title	Geometry of hypersurfaces
title_auth	Geometry of hypersurfaces
title_exact_search	Geometry of hypersurfaces
title_full	Geometry of hypersurfaces Thomas E. Cecil, Patrick J. Ryan
title_fullStr	Geometry of hypersurfaces Thomas E. Cecil, Patrick J. Ryan
title_full_unstemmed	Geometry of hypersurfaces Thomas E. Cecil, Patrick J. Ryan
title_short	Geometry of hypersurfaces
title_sort	geometry of hypersurfaces
topic	Mathematics Topological groups Lie groups Differential geometry Hyperbolic geometry Differential Geometry Topological Groups, Lie Groups Hyperbolic Geometry Mathematik
topic_facet	Mathematics Topological groups Lie groups Differential geometry Hyperbolic geometry Differential Geometry Topological Groups, Lie Groups Hyperbolic Geometry Mathematik
url	https://doi.org/10.1007/978-1-4939-3246-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632857&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632857&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT cecilthomase geometryofhypersurfaces AT ryanpatrickj geometryofhypersurfaces

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