Verfügbarkeit: Intrinsic geometry of surfaces

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Titel:	Intrinsic geometry of surfaces
Von:	by A. D. Aleksandrov and V. A. Zalgaller
Person:	Aleksandrov, Aleksandr D. 1912-1999 Verfasser aut Zalgaller, V. A. 1920-2020
Hauptverfassende:	Aleksandrov, Aleksandr D. 1912-1999 (VerfasserIn), Zalgaller, V. A. 1920-2020 (VerfasserIn)
Format:	Buch
Sprache:	Englisch Russisch
Veröffentlicht:	Providence, R.I. American Math. Soc. 1967
Schriftenreihe:	Translations of mathematical monographs 15.
Notation:	SK 370
Schlagwörter:	Geometria Diferencial Géométrie différentielle Geometry, Differential Mannigfaltigkeit Oberfläche Krümmung Dimension 2 Differentialgeometrie Wirkliche Geometrie
Medienzugang:	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
Beschreibung:	Aus d. Russ. übers.
Umfang:	VI, 327 S. graph. Darst.

Internformat

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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
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author	Aleksandrov, Aleksandr D. 1912-1999 Zalgaller, V. A. 1920-2020
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genre	Wirkliche Geometrie gnd
genre_facet	Wirkliche Geometrie
id	DE-604.BV005693090
illustrated	Illustrated
indexdate	2024-12-20T08:36:51Z
institution	BVB
language	English Russian
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-003555757
oclc_num	251423061
open_access_boolean
owner	DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-384 DE-91G DE-BY-TUM DE-29T DE-83 DE-188
owner_facet	DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-384 DE-91G DE-BY-TUM DE-29T DE-83 DE-188
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
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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