Elementary differential geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 473 S. Ill., graph. Darst. |
| ISBN: | 9781848828902 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | ANDREW PRESSLEY ELEMENTARY DIFFERENTIAL GEOMETRY SECOND EDITION
TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATS8IBIJOTHEK HANNOVER V I J
SPRINGER CONTENTS PREFACE CONTENTS 1. CURVES IN THE PLANE AND IN SPACE
1.1 WHAT IS A CURVE? 1 1.2 ARC-LENGTH 9 1.3 REPARAMETRIZATION 13 1.4
CLOSED CURVES 19 1.5 LEVEL CURVES VERSUS PARAMETRIZED CURVES 23 2. HOW
MUCH DOES A CURVE CURVE? 2.1 CURVATURE 29 2.2 PLANE CURVES 34 2.3 SPACE
CURVES 46 3. GLOBAL PROPERTIES OF CURVES 3.1 SIMPLE CLOSED CURVES 55 3.2
THE ISOPERIMETRIC INEQUALITY 58 3.3 THE FOUR VERTEX THEOREM 62 4.
SURFACES IN THREE DIMENSIONS 4.1 WHAT IS A SURFACE? 67 4.2 SMOOTH
SURFACES 76 4.3 SMOOTHMAPS 82 4.4 TANGENTS AND DERIVATIVES 85 4.5
NORMALS AND ORIENTABILITY 89 IX X CONTENTS 5. EXAMPLES OF SURFACES 5.1
LEVEL SURFACES 95 5.2 QUADRIC SURFACES 97 5.3 RULED SURFACES AND
SURFACES OF REVOLUTION 104 5.4 COMPACT SURFACES 109 5.5 TRIPLY
ORTHOGONAL SYSTEMS ILL 5.6 APPLICATIONS OF THE INVERSE FUNCTION THEOREM
116 6. THE FIRST FUNDAMENTAL FORM 6.1 LENGTHS OF CURVES ON SURFACES 121
6.2 ISOMETRIES OF SURFACES 126 6.3 CONFERMAL MAPPINGS OF SURFACES 133
6.4 EQUIAREALMAPS AND A THEOREM OF ARCHIMEDES 139 6.5 SPHERICAL GEOMETRY
148 7. CURVATURE OF SURFACES 7.1 THE SECOND FUNDAMENTAL FORM 159 7.2 THE
GAUSS AND WEINGARTEN MAPS 162 7.3 NORMAL AND GEODESIC CURVATURES 165 7.4
PARALLEL TRANSPORT AND COVARIANT DERIVATIVE 170 8. GAUSSIAN, MEAN AND
PRINCIPAL CURVATURES 8.1 GAUSSIAN AND MEAN CURVATURES 179 8.2 PRINCIPAL
CURVATURES OF A SURFACE 187 8.3 SURFACES OF CONSTANT GAUSSIAN CURVATURE
196 8.4 FLAT SURFACES 201 8.5 SURFACES OF CONSTANT MEAN CURVATURE 206
8.6 GAUSSIAN CURVATURE OF COMPACT SURFACES 212 9. GEODESIES 9.1
DEFINITION AND BASIC PROPERTIES 215 9.2 GEODESIC EQUATIONS 220 9.3
GEODESIES ON SURFACES OF REVOLUTION 227 9.4 GEODESIES AS SHORTEST PATHS
235 9.5 GEODESIC COORDINATES 242 10. GAUSS THEOREMA EGREGIUM 10.1 THE
GAUSS AND CODAZZI-MAINARDI EQUATIONS 247 10.2 GAUSS REMARKABLE THEOREM
252 10.3 SURFACES OF CONSTANT GAUSSIAN CURVATURE 257 10.4 GEODESIC
MAPPINGS 263 CONTENTS XI 11. HYPERBOLIC GEOMETRY 11.1 UPPER HALF-PLANE
MODEL 270 11.2 ISOMETRIES OF% 277 11.3 POINCARE DISC MODEL 283 11.4
HYPERBOLIC PARALLELS 290 11.5 BELTRAMI-KLEIN MODEL 295 12. MINIMAL
SURFACES 12.1 PLATEAU S PROBLEM 305 12.2 EXAMPLES OF MINIMAL SURFACES
....312 12.3 GAUSS MAP OF A MINIMAL SURFACE 320 12.4 CONFORMAL
PARAMETRIZATION OF MINIMAL SURFACES 322 12.5 MINIMAL SURFACES AND
HOLOMORPHIC FUNCTIONS 325 13. THE GAUSS-BONNET THEOREM 13.1 GAUSS-BONNET
FOR SIMPLE CLOSED CURVES 335 13.2 GAUSS-BONNET FOR CURVILINEAR POLYGONS
342 13.3 INTEGRATION ON COMPACT SURFACES 346 13.4 GAUSS-BONNET FOR
COMPACT SURFACES 349 13.5 MAP COLOURING 357 13.6 HOLONOMY AND GAUSSIAN
CURVATURE 362 13.7 SINGULARITIES OF VECTOR FIELDS 365 13.8 CRITICAL
POINTS 372 AO. INNER PRODUCT SPACES AND SELF-ADJOINT LINEAR MAPS AL.
ISOMETRIES OF EUCLIDEAN SPACES A2. MOBIUS TRANSFORMATIONS HINTS TO
SELECTED EXERCISES SOLUTIONS INDEX
|
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| ctrlnum | (OCoLC)436030854 (DE-599)BVBBV035750740 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:39Z |
| institution | BVB |
| isbn | 9781848828902 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018610795 |
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| physical | XI, 473 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
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| series2 | Springer undergraduate mathematics series |
| spelling | Pressley, Andrew Verfasser (DE-588)122153049 aut Elementary differential geometry Andrew Pressley 2. ed. London [u.a.] Springer 2010 XI, 473 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-84882-891-9 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018610795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pressley, Andrew Elementary differential geometry Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4123623-3 |
| title | Elementary differential geometry |
| title_auth | Elementary differential geometry |
| title_exact_search | Elementary differential geometry |
| title_full | Elementary differential geometry Andrew Pressley |
| title_fullStr | Elementary differential geometry Andrew Pressley |
| title_full_unstemmed | Elementary differential geometry Andrew Pressley |
| title_short | Elementary differential geometry |
| title_sort | elementary differential geometry |
| topic | Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Differentialgeometrie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018610795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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