General theory of irregular curves:
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht ; Boston
Kluwer Academic Publishers
[c1989]
|
| Series: | Mathematics and its applications / Soviet series
29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 288 Seiten Illustrationen, Diagramme 25 cm |
| ISBN: | 9027728119 |
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MARC
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| 245 | 1 | 0 | |a General theory of irregular curves |c A. D. Alexandrov and Yu. G. Reshetnyak. [Translated from the Russian by L.Ya. Yuzina] |
| 264 | 1 | |a Dordrecht ; Boston |b Kluwer Academic Publishers |c [c1989] | |
| 300 | |a X, 288 Seiten |b Illustrationen, Diagramme |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 29 | |
| 650 | 4 | |a Courbes sur les surfaces | |
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Record in the Search Index
| _version_ | 1804118419868483584 |
|---|---|
| adam_text | Table of Contents
Series Editor s Preface ix
Introduction 1
Chapter I: General Notion of a Curve 5
1.1. Definition of a Curve 5
1.2. Normal Parametrization of a Curve 15
1.3. Chains on a Curve and the Notion of an Inscribed Polygonal Line 16
1.4. Distance Between Curves and Curve Convergence 18
1.5. On a Non Parametric Definition of the Notion of a Curve 23
Chapter II: Length of a Curve 29
2.1. Definition of a Curve Length and its Basic Properties 29
2.2. Rectifiable Curves in Euclidean Spaces 33
2.3. Rectifiable Curves in Lipshitz Manifolds 40
Chapter III: Tangent and the Class of One Sidedly
Smooth Curves 43
3.1. Definition and Basic Properties of One Sidedly Smooth Curves 43
3.2. Projection Criterion of the Existence of a Tangent in the Strong
Sense 47
3.3. Characterizing One Sidedly Smooth Curves with Contingencies 49
3.4. One Sidedly Smooth Functions 54
3.5. Notion of c Correspondence. Indicatrix of Tangents of a Curve 55
3.6. One Sidedly Smooth Curves in Differentiable Manifolds 63
Chapter IV: Some Facts of Integral Geometry 75
4.1. Manifold Gy. of fc Dimensional Directions in V 75
4.2. Imbedding of G% into a Euclidean Space 80
4.3. Existence of Invariant Measure of 6* 85
4.4. Invariant Measure in G% and Integral. Uniqueness of an Invariant
Measure 88
4.5. Some Relations for Integrals Relative to the Invariant Measure in CJ! 93
4.6. Some Specific Subsets of G£ 96
4.7. Length of a Spherical Curve as an Integral of the
Function Equal to the Number of Intersection Points 101
4.8. Length of a Curve as an Integral of Lengths of its Projections 105
vi TABLE OF CONTENTS
4.9. Generalization of Theorems on the Mean Number of the Points of
Intersection and Other Problems 109
Chapter V: Turn or Integral Curvature of a Curve 118
5.1. Definition of a Turn. Basic Properties of Curves of a Finite Turn 118
5.2. Definition of a Turn of a Curve by Contingencies 127
5.3. Turn of a Regular Curve 132
5.4. Analytical Criterion of Finiteness of a Curve Turn 134
5.5. Basic Integro Geometrical Theorem on a Curve Turn 139
5.6. Some Estimates and Theorems on a Limiting Transition 144
5.7. Turn of a Curve as a Limit of the Sum of Angles Between the Secants 148
5.8. Exact Estimates of the Length of a Curve 151
5.9. Convergence with a Turn 160
5.10 Turn of a Plane Curve 164
Chapter VI: Theory of a Turn on an n Dimensional
Sphere 175
6.1. Auxiliary Results 175
6.2. Integro Geometrical Theorem on Angles and its Corrolaries 184
6.3. Definition and Basic Properties of Spherical Curves of a Finite
Geodesic Turn 191
6.4. Definition of a Geodesic Turn by Means of Tangents 197
6.5. Curves on a Two Dimensional Sphere 203
Chapter VII: Osculating Planes and Class of Curves with
an Osculating Plane in the Strong Sense 208
7.1. Notion of an Osculating Plane 208
7.2. Osculating Plane of a Plane Curve 211
7.3. Properties of Curves with an Osculating Plane in the Strong Sense 214
Chapter VIII: Torsion of a Curve in a Three
Dimensional Euclidean Space 217
8.1. Torsion of a Plane Curve 217
8.2. Curves of a Finite Complete Torsion 243
8.3. Complete Two Dimensional Indicatrix of a Curve of a Finite
Complete Torsion 249
8.4. Continuity and Additivity of Absolute Torsion 254
8.5. Definition of an Absolute Torsion Through Triple Chains and
Paratingences 255
8.6. Right Hand and Left Hand Indices of a Point. Complete Torsion
of a Curve 257
TABLE OF CONTENTS vii
Chapter IX: Frenet Formulas and Theorems on Natural
Parametrization 268
9.1. Frenet Formulas 268
9.2. Theorems on Natural Parametrization 275
Chapter X: Some Additional Remarks 281
References 285
Index 287
|
| any_adam_object | 1 |
| author | Aleksandrov, Aleksandr D. 1912-1999 Rešetnjak, Jurij Grigorʹevič 1929- |
| author2 | Juzina, L. Ja. 19XX- |
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| author_facet | Aleksandrov, Aleksandr D. 1912-1999 Rešetnjak, Jurij Grigorʹevič 1929- Juzina, L. Ja. 19XX- |
| author_role | aut aut |
| author_sort | Aleksandrov, Aleksandr D. 1912-1999 |
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| 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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004219388 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:10:00Z |
| institution | BVB |
| isbn | 9027728119 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002627114 |
| oclc_num | 18290200 |
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| physical | X, 288 Seiten Illustrationen, Diagramme 25 cm |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Aleksandrov, Aleksandr D. 1912-1999 Verfasser (DE-588)117706671 aut General theory of irregular curves A. D. Alexandrov and Yu. G. Reshetnyak. [Translated from the Russian by L.Ya. Yuzina] Dordrecht ; Boston Kluwer Academic Publishers [c1989] X, 288 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 29 Courbes sur les surfaces Courbes sur les surfaces ram Curves on surfaces Integralgeometrie (DE-588)4161911-0 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Integralgeometrie (DE-588)4161911-0 s Kurve (DE-588)4033824-1 s DE-604 Rešetnjak, Jurij Grigorʹevič 1929- Verfasser (DE-588)1089148887 aut Juzina, L. Ja. 19XX- (DE-588)1296363422 trl Soviet series Mathematics and its applications 29 (DE-604)BV004708148 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002627114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aleksandrov, Aleksandr D. 1912-1999 Rešetnjak, Jurij Grigorʹevič 1929- General theory of irregular curves Courbes sur les surfaces Courbes sur les surfaces ram Curves on surfaces Integralgeometrie (DE-588)4161911-0 gnd Kurve (DE-588)4033824-1 gnd |
| subject_GND | (DE-588)4161911-0 (DE-588)4033824-1 |
| title | General theory of irregular curves |
| title_auth | General theory of irregular curves |
| title_exact_search | General theory of irregular curves |
| title_full | General theory of irregular curves A. D. Alexandrov and Yu. G. Reshetnyak. [Translated from the Russian by L.Ya. Yuzina] |
| title_fullStr | General theory of irregular curves A. D. Alexandrov and Yu. G. Reshetnyak. [Translated from the Russian by L.Ya. Yuzina] |
| title_full_unstemmed | General theory of irregular curves A. D. Alexandrov and Yu. G. Reshetnyak. [Translated from the Russian by L.Ya. Yuzina] |
| title_short | General theory of irregular curves |
| title_sort | general theory of irregular curves |
| topic | Courbes sur les surfaces Courbes sur les surfaces ram Curves on surfaces Integralgeometrie (DE-588)4161911-0 gnd Kurve (DE-588)4033824-1 gnd |
| topic_facet | Courbes sur les surfaces Curves on surfaces Integralgeometrie Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002627114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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