Intrinsic geometry of surfaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, R.I.
American Math. Soc.
1967
|
| Series: | Translations of mathematical monographs
15. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | VI, 327 S. graph. Darst. |
Staff View
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| 240 | 1 | 0 | |a Dvumernye mnogoobrazija ograničennoj krivizny |
| 245 | 1 | 0 | |a Intrinsic geometry of surfaces |c by A. D. Aleksandrov and V. A. Zalgaller |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 1967 | |
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Record in the Search Index
| _version_ | 1804119880318844928 |
|---|---|
| adam_text | TABLE OF CONTENTS
Introduction v
Chapter I. The Simplest Concepts and the Object
of the Investigation 1
1. The intrinsic metric of a space 1
2. Two dimensional manifolds of bounded curvature 4
3. Approximation by polyhedral metrics 7
4. Quantitative characteristics of figures 9
5. Cutting and pasting 12
6. Further investigations 14
Chapter II. Angle 20
1. Properties of the upper angle 20
2. Lower strong angle •. 27
3. Fundamental theorems on the angles of a triangle 29
4. Criteria for existence of the angle 34
5. Angle of a sector 39
Chapter III. Approximation by Polyhedral Metrics 48
1. Neighborhood of a point 48
2. Triangulation 58
3. Excesses of the triangles of the triangulation 63
4. Development constructed with respect to a triangulation ... 69
5. Some properties of a polyhedral metric 71
6. Approximation by polyhedral metrics 79
Chapter IV. Metrics Admitting Approximation by
Polyhedral Metrics 90
1. Convergent metrics and the limit metric 90
2. Two estimates for polyhedral metrics 98
3. Existence of angles in the limit metric 115
4. Sector angle 118
5. Boundedness of the absolute curvature of the
approximating metric 124
6. Further information on angles 126
7. Excesses of nonoverlapping triangles 134
iii
iv TABLE OF CONTENTS
Chapter V. Curvature 147
1. On a method of introducing measure 147
2. Definition of curvature 153
3. Other definitions of curvature 156
4. Some preliminary estimates 176
Chapter VI. Rotation of Curves. Pasting of Manifolds 180
1. Direction and rotation of curves 180
2. Connection between rotation and curvature 188
3. Rotation of shortest arcs 192
4. Pasting together of polygons 202
5. Estimation of the excesses and the distortion of
angles in terms of the curvature 214
Chapter VII. Converging Metrics 222
1. Convergence of metrics 222
2. Converging curves and polygons 225
3. Charges and weak convergence 233
4. Curvatures of converging metrics 236
5. Regular convergence 244
6. Convergence of angles 250
Chapter VIII. Area 255
1. Triangles in polyhedral metrics 255
2. Definition of area 260
3. Convergence of areas 267
Chapter IX. Curves with Rotation of Bounded Variation .... 272
1. Variation of the rotation 272
2. Approximation by polygonal curves 278
3. Second theorem on pasting 288
4. Converging curves 296
5. Possible extensions of the class of curves with
rotations of bounded variation 307
Complements to Chapter II. On various definitions of the angle . . 310
Bibliography 321
Subject Index 325
|
| any_adam_object | 1 |
| author | Aleksandrov, Aleksandr D. 1912-1999 Zalgaller, V. A. 1920-2020 |
| author_GND | (DE-588)117706671 (DE-588)111128587 |
| author_facet | Aleksandrov, Aleksandr D. 1912-1999 Zalgaller, V. A. 1920-2020 |
| author_role | aut aut |
| author_sort | Aleksandrov, Aleksandr D. 1912-1999 |
| author_variant | a d a ad ada v a z va vaz |
| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 533f |
| ctrlnum | (OCoLC)251423061 (DE-599)BVBBV005693090 |
| dewey-full | 516/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.7 |
| dewey-search | 516/.7 |
| dewey-sort | 3516 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Wirkliche Geometrie gnd |
| genre_facet | Wirkliche Geometrie |
| id | DE-604.BV005693090 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:13Z |
| institution | BVB |
| language | English Russian |
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| physical | VI, 327 S. graph. Darst. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Aleksandrov, Aleksandr D. 1912-1999 Verfasser (DE-588)117706671 aut Dvumernye mnogoobrazija ograničennoj krivizny Intrinsic geometry of surfaces by A. D. Aleksandrov and V. A. Zalgaller Providence, R.I. American Math. Soc. 1967 VI, 327 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 15. Aus d. Russ. übers. Geometria Diferencial larpcal Géométrie différentielle Geometry, Differential Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Krümmung (DE-588)4128765-4 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Wirkliche Geometrie gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Oberfläche (DE-588)4042907-6 s Wirkliche Geometrie f Krümmung (DE-588)4128765-4 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 2 (DE-588)4321721-7 s 1\p DE-604 Zalgaller, V. A. 1920-2020 Verfasser (DE-588)111128587 aut Translations of mathematical monographs 15. (DE-604)BV000002394 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003555757&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aleksandrov, Aleksandr D. 1912-1999 Zalgaller, V. A. 1920-2020 Intrinsic geometry of surfaces Translations of mathematical monographs Geometria Diferencial larpcal Géométrie différentielle Geometry, Differential Mannigfaltigkeit (DE-588)4037379-4 gnd Oberfläche (DE-588)4042907-6 gnd Krümmung (DE-588)4128765-4 gnd Dimension 2 (DE-588)4321721-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4042907-6 (DE-588)4128765-4 (DE-588)4321721-7 (DE-588)4012248-7 |
| title | Intrinsic geometry of surfaces |
| title_alt | Dvumernye mnogoobrazija ograničennoj krivizny |
| title_auth | Intrinsic geometry of surfaces |
| title_exact_search | Intrinsic geometry of surfaces |
| title_full | Intrinsic geometry of surfaces by A. D. Aleksandrov and V. A. Zalgaller |
| title_fullStr | Intrinsic geometry of surfaces by A. D. Aleksandrov and V. A. Zalgaller |
| title_full_unstemmed | Intrinsic geometry of surfaces by A. D. Aleksandrov and V. A. Zalgaller |
| title_short | Intrinsic geometry of surfaces |
| title_sort | intrinsic geometry of surfaces |
| topic | Geometria Diferencial larpcal Géométrie différentielle Geometry, Differential Mannigfaltigkeit (DE-588)4037379-4 gnd Oberfläche (DE-588)4042907-6 gnd Krümmung (DE-588)4128765-4 gnd Dimension 2 (DE-588)4321721-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometria Diferencial Géométrie différentielle Geometry, Differential Mannigfaltigkeit Oberfläche Krümmung Dimension 2 Differentialgeometrie Wirkliche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003555757&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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