Geometry of hypersurfaces:
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York ; Heidelberg ; Dordrecht ; London
Springer
[2015]
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 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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Record in the Search Index
| _version_ | 1804175709033201664 |
|---|---|
| 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.
|
| any_adam_object | 1 |
| author | Cecil, Thomas E. 1945- Ryan, Patrick J. |
| author_GND | (DE-588)102959354X (DE-588)108226007X |
| author_facet | Cecil, Thomas E. 1945- Ryan, Patrick J. |
| author_role | aut aut |
| author_sort | Cecil, Thomas E. 1945- |
| author_variant | t e c te tec p j r pj pjr |
| building | Verbundindex |
| bvnumber | BV043209697 |
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| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)930013721 (DE-599)BVBBV043209697 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4939-3246-7 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:20:35Z |
| institution | BVB |
| isbn | 9781493932467 |
| issn | 1439-7382 |
| language | English |
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| spelling | Cecil, Thomas E. 1945- (DE-588)102959354X aut Geometry of hypersurfaces Thomas E. Cecil, Patrick J. Ryan New York ; Heidelberg ; Dordrecht ; London Springer [2015] © 2015 1 Online Ressource (XI, 596 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics 1439-7382 Mathematics Topological groups Lie groups Differential geometry Hyperbolic geometry Differential Geometry Topological Groups, Lie Groups Hyperbolic Geometry Mathematik Ryan, Patrick J. (DE-588)108226007X aut Erscheint auch als Druck-Ausgabe 978-1-4939-3245-0 Erscheint auch als Druckausgabe 978-1-4939-3245-0 https://doi.org/10.1007/978-1-4939-3246-7 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf 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 Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf 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 Abstract |
| 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 |
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