Differential geometry: curves, surfaces, manifolds
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Student mathematical library
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 380 S. graph. Darst. |
| ISBN: | 0821839888 9780821839881 |
Internformat
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| 100 | 1 | |a Kühnel, Wolfgang |d 1950- |e Verfasser |0 (DE-588)133800849 |4 aut | |
| 240 | 1 | 0 | |a Differentialgeometrie |
| 245 | 1 | 0 | |a Differential geometry |b curves, surfaces, manifolds |c Wolfgang Kühnel. Transl. by Bruce Hunt |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 2006 | |
| 300 | |a XII, 380 S. |b graph. Darst. | ||
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| 650 | 4 | |a Surfaces (Mathématiques) | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 4 | |a Curves | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Surfaces | |
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Datensatz im Suchindex
| _version_ | 1804135547448328192 |
|---|---|
| adam_text | Contents
Preface to the English Edition
Preface to the German Edition
Chapter
Chapter
2A Frenet curves in JRn
2B Plane curves and space curves
2C Relations between the curvature and the torsion
2D The Frenet equations and the fundamental theorem
of the local theory of curves
2E Curves in Minkowski space IRf
2F The global theory of curves
Exercises
Chapter
ЗА
3B The Gauss map and the curvature of surfaces
3C Surfaces of rotation and ruled surfaces
3D
3E Surfaces in Minkowski space J?.f
vj
3F
Exercises
Chapter
4A The covariant derivative
4B Parallel displacement and geodesies
4C The Gaussian equation and the
4D The fundamental theorem of the local theory of surfaces
4E The Gaussian curvature in special parameters
4F The GauHS-Bonnet Theorem
4G Selected topics in the global theory of surfaces
Exercises
Chapter
5A The notion of a manifold
5B The tangent space
5C Riemannian metrics
5D The Riemannian connection
Exercises
Chapter
6A Tensors
6B The sectional curvature
6C The
Exercises
Chapter
7A Hyperbolic space
7B Geodesies and Jacobi fields
7C The space form problem
7D Three-dimensional Euclidean and spherical space forms
Exercises
Contents
Chapter
8A The variation of the
8B The Einstein field equations
8C Homogeneous Einstein spaces
8D The decomposition of the curvature tensor
8E The Weyl tensor
8F Duality for four-manifolds and
Exercises
Bibliography
List of notation
Index
This carefully written book is an introduction to the beau¬
tiful ideas and results of differential geometry The first half
covers the geometry of curves and surfaces, which provide
much of the motivation and intuition for the general theory.
Special topics that are explored include Frenet frames, ruled
surfaces, minimal surfaces, and the Gauss-Bonnet theorem.
The second part is an introduction to the geometry of
general manifolds, with particular emphasis on connections
and curvature. The final two chapters are insightful examina¬
tions of the special cases of spaces of constant curvature and
Einstein manifolds.
The text is illustrated with many figures and examples. For
the second edition, a number of errors were corrected and
some text and a number of figures have been added. The
prerequisites are undergraduate analysis and linear algebra.
|
| adam_txt |
Contents
Preface to the English Edition
Preface to the German Edition
Chapter
Chapter
2A Frenet curves in JRn
2B Plane curves and space curves
2C Relations between the curvature and the torsion
2D The Frenet equations and the fundamental theorem
of the local theory of curves
2E Curves in Minkowski space IRf
2F The global theory of curves
Exercises
Chapter
ЗА
3B The Gauss map and the curvature of surfaces
3C Surfaces of rotation and ruled surfaces
3D
3E Surfaces in Minkowski space J?.f
vj
3F
Exercises
Chapter
4A The covariant derivative
4B Parallel displacement and geodesies
4C The Gaussian equation and the
4D The fundamental theorem of the local theory of surfaces
4E The Gaussian curvature in special parameters
4F The GauHS-Bonnet Theorem
4G Selected topics in the global theory of surfaces
Exercises
Chapter
5A The notion of a manifold
5B The tangent space
5C Riemannian metrics
5D The Riemannian connection
Exercises
Chapter
6A Tensors
6B The sectional curvature
6C The
Exercises
Chapter
7A Hyperbolic space
7B Geodesies and Jacobi fields
7C The space form problem
7D Three-dimensional Euclidean and spherical space forms
Exercises
Contents
Chapter
8A The variation of the
8B The Einstein field equations
8C Homogeneous Einstein spaces
8D The decomposition of the curvature tensor
8E The Weyl tensor
8F Duality for four-manifolds and
Exercises
Bibliography
List of notation
Index
This carefully written book is an introduction to the beau¬
tiful ideas and results of differential geometry The first half
covers the geometry of curves and surfaces, which provide
much of the motivation and intuition for the general theory.
Special topics that are explored include Frenet frames, ruled
surfaces, minimal surfaces, and the Gauss-Bonnet theorem.
The second part is an introduction to the geometry of
general manifolds, with particular emphasis on connections
and curvature. The final two chapters are insightful examina¬
tions of the special cases of spaces of constant curvature and
Einstein manifolds.
The text is illustrated with many figures and examples. For
the second edition, a number of errors were corrected and
some text and a number of figures have been added. The
prerequisites are undergraduate analysis and linear algebra. |
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| author | Kühnel, Wolfgang 1950- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)61500086 (DE-599)BVBBV021711017 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:20:28Z |
| indexdate | 2024-07-09T20:42:14Z |
| institution | BVB |
| isbn | 0821839888 9780821839881 |
| language | German English |
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| physical | XII, 380 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | American Mathematical Soc. |
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| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Kühnel, Wolfgang 1950- Verfasser (DE-588)133800849 aut Differentialgeometrie Differential geometry curves, surfaces, manifolds Wolfgang Kühnel. Transl. by Bruce Hunt 2. ed. Providence, RI American Mathematical Soc. 2006 XII, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 16 Courbes Geometria diferencial larpcal Géométrie différentielle Surfaces (Mathématiques) Variétés (Mathématiques) Curves Geometry, Differential Manifolds (Mathematics) Surfaces Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s DE-604 Student mathematical library 16 (DE-604)BV013184751 16 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014924836&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014924836&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kühnel, Wolfgang 1950- Differential geometry curves, surfaces, manifolds Student mathematical library Courbes Geometria diferencial larpcal Géométrie différentielle Surfaces (Mathématiques) Variétés (Mathématiques) Curves Geometry, Differential Manifolds (Mathematics) Surfaces Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4123623-3 |
| title | Differential geometry curves, surfaces, manifolds |
| title_alt | Differentialgeometrie |
| title_auth | Differential geometry curves, surfaces, manifolds |
| title_exact_search | Differential geometry curves, surfaces, manifolds |
| title_exact_search_txtP | Differential geometry curves, surfaces, manifolds |
| title_full | Differential geometry curves, surfaces, manifolds Wolfgang Kühnel. Transl. by Bruce Hunt |
| title_fullStr | Differential geometry curves, surfaces, manifolds Wolfgang Kühnel. Transl. by Bruce Hunt |
| title_full_unstemmed | Differential geometry curves, surfaces, manifolds Wolfgang Kühnel. Transl. by Bruce Hunt |
| title_short | Differential geometry |
| title_sort | differential geometry curves surfaces manifolds |
| title_sub | curves, surfaces, manifolds |
| topic | Courbes Geometria diferencial larpcal Géométrie différentielle Surfaces (Mathématiques) Variétés (Mathématiques) Curves Geometry, Differential Manifolds (Mathematics) Surfaces Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Courbes Geometria diferencial Géométrie différentielle Surfaces (Mathématiques) Variétés (Mathématiques) Curves Geometry, Differential Manifolds (Mathematics) Surfaces Differentialgeometrie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014924836&sequence=000002&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=014924836&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
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