A study of surfaces in an elliptic space:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Delhi
Hindustan Publ.Corp.
1964
|
| Series: | Internat.monographs on advanced mathematics and physics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Nekotor'e vopros teorii poverchnostej na elliptičeskom prostranstve (engl.) |
| Physical Description: | VIII,94 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a A study of surfaces in an elliptic space |c Aleksej Vasil'evič Pogorelov* |
| 264 | 1 | |a Delhi |b Hindustan Publ.Corp. |c 1964 | |
| 300 | |a VIII,94 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Internat.monographs on advanced mathematics and physics. | |
| 500 | |a EST: Nekotor'e vopros teorii poverchnostej na elliptičeskom prostranstve (engl.) | ||
| 650 | 4 | |a Convex surfaces | |
| 650 | 4 | |a Elliptic space | |
| 650 | 0 | 7 | |a Fläche |0 (DE-588)4129864-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804119894557458432 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Elliptic Space
1. Four dimensional vector space 3
2. Concept of an elliptic space 6
3. Curves in the ellipti cspace 9
4. Surfaces in the elliptic space 13
5. Fundamental equations of the theory of surfaces in an
elliptic space 16
Chapter 2. Convex Bodies and Convex Surfaces in an
Elliptic Space
1. Concept of a convex body 19
2. Convex surfaces in an elliptic space 21
3. On the deviation of the shortest line on a convex surface
from its semi tangent at the initial point . . . .24
4. Manifolds of curvature not less than K The theorems of
A. D. Alexandrov 26
Chapter 3. Transformation of Congruent Figures
1. Transformation of congruent figures in an elliptic space
into congruent figures in a Euclidean space . .31
2. Transformation of congruent figures in the Euclidean space
into congruent figures in the elliptic space . . . .34
3. Transformation of infinitesimal displacements . . .37
4. Transformation of straight lines and planes . . .40
Chapter 4. Isometric Surfaces
1. Transformation of isometric surfaces .... 44
viii
2. Transformation of locally convex isometric surfaces in an
elliptic space 47
3 Proof of lemma 1 49
4. Transformation of locally convex isometric surfaces in a
Euclidean space 52
5. Proof of lemma 2 54
Chapter 5. Infinitesimal Deformations of Surfaces in an
Elliptic Space
1. Pairs of isometric surfaces and infinitesimal deformations 57
2. Transformation of surfaces and their infinitesimal deforma¬
tions 59
3. Some theorems on the infinitesimal deformations of surfaces
in an elliptic space 62
Chapter 6. Unique Determination of General Convex
Surfaces in the Elliptic Space
1. A lemma on the ridge points of a convex surface . . 65
2. Transformation of isometric dihedral angles and cones 67
3. Local convexity of surfaces 4 i and t 2 at the smooth points 70
4. Convexity and isometry of the surfaces $1 and J 2 . .72
5. Various theorems on the unique determination of convex
surfaces in the elliptic space 75
Chapter 7. Regularity of Convex Surfaces with a
Regular Metric
1. Equation of deformation of surfaces in the elliptic space 79
2. Evaluation of the normal curvature of a regular convex cap
in the elliptic space 82
3. Convex surfaces of a bounded specific curvature in the
elliptic space 85
4. Proof of the regularity of convex surfaces with a regular
metric in the elliptic space 88
References 92
Index 93
|
| any_adam_object | 1 |
| author | Pogorelov, Aleksej V. 1919-2002 |
| author_GND | (DE-588)123013453 |
| author_facet | Pogorelov, Aleksej V. 1919-2002 |
| author_role | aut |
| author_sort | Pogorelov, Aleksej V. 1919-2002 |
| author_variant | a v p av avp |
| building | Verbundindex |
| bvnumber | BV005708059 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA689 |
| callnumber-search | QA689 |
| callnumber-sort | QA 3689 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)2183884 (DE-599)BVBBV005708059 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005708059 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:27Z |
| institution | BVB |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003565800 |
| oclc_num | 2183884 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-188 |
| physical | VIII,94 S. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Hindustan Publ.Corp. |
| record_format | marc |
| series2 | Internat.monographs on advanced mathematics and physics. |
| spelling | Pogorelov, Aleksej V. 1919-2002 Verfasser (DE-588)123013453 aut A study of surfaces in an elliptic space Aleksej Vasil'evič Pogorelov* Delhi Hindustan Publ.Corp. 1964 VIII,94 S. txt rdacontent n rdamedia nc rdacarrier Internat.monographs on advanced mathematics and physics. EST: Nekotor'e vopros teorii poverchnostej na elliptičeskom prostranstve (engl.) Convex surfaces Elliptic space Fläche (DE-588)4129864-0 gnd rswk-swf Elliptischer Raum (DE-588)4456592-6 gnd rswk-swf Elliptischer Raum (DE-588)4456592-6 s Fläche (DE-588)4129864-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pogorelov, Aleksej V. 1919-2002 A study of surfaces in an elliptic space Convex surfaces Elliptic space Fläche (DE-588)4129864-0 gnd Elliptischer Raum (DE-588)4456592-6 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4456592-6 |
| title | A study of surfaces in an elliptic space |
| title_auth | A study of surfaces in an elliptic space |
| title_exact_search | A study of surfaces in an elliptic space |
| title_full | A study of surfaces in an elliptic space Aleksej Vasil'evič Pogorelov* |
| title_fullStr | A study of surfaces in an elliptic space Aleksej Vasil'evič Pogorelov* |
| title_full_unstemmed | A study of surfaces in an elliptic space Aleksej Vasil'evič Pogorelov* |
| title_short | A study of surfaces in an elliptic space |
| title_sort | a study of surfaces in an elliptic space |
| topic | Convex surfaces Elliptic space Fläche (DE-588)4129864-0 gnd Elliptischer Raum (DE-588)4456592-6 gnd |
| topic_facet | Convex surfaces Elliptic space Fläche Elliptischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pogorelovaleksejv astudyofsurfacesinanellipticspace |