Hyperbolic geometry and barbilian spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Palm Harbor, FL
Hadronic Press
1996
|
| Schriftenreihe: | Series of monographs in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 161 S. graph. Darst. |
| ISBN: | 1574850075 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804126718064066560 |
|---|---|
| adam_text | SERIES OF MONOGRAPHS IN ADVANCED MATHEMATICS ISTTTUTO PER LA RICERCA DI
BASE CASTELLO PRINCIPE PIGNATELLI, 86075 MONTERODUNI (IS), MOLISE, ITALY
HYPERBOLIC GEOMETRY AND BARBILIAN SPACES WLADIMIR-GEORGE BOSKOFF FACULTY
OF MATHEMATICS UNIVERSITY OVIDIUS OF CONSTANTA 124 BD MAMAIA, 8700
CONSTANTA, RUMANIA HADRONIC PRESS CONTENTS CHAPTER ONE PROJECTIVE AND
HYPERBOLIC GEOMETRY 1.1. ANHARMONIC RATIO AND INFINITE POINTS FOR
STRAIGHT LINES 1 1.2. EULER S IDENTITY AND THE STRUCTURE OF O 4 2 1.3.
THE NUMBER OF DISTINCT ANHARMONIC RATII RELATIVE TO A GIVEN DIVISION 5
1.4. HARMONIC AND EQIHARMONIC DIVISIONS 7 1.5. THE EXTENSION OF THE
CONCEPT OF ANHARMONIC RATIO 9 1.6. PROJECTIVITY, PERSPECTIVITY AND
APPLICATIONS. THE INFINITE STRAIGHT LINE OF THE PLANE. DUALITY. 11 1.7.
IMAGINARY ELEMENTS IN GEOMETRY. CIRCULAR POINTS OF THE PLANE 19 1.8. THE
HESSE S POINTS 23 1.9. PROJECTIVITIES ON A CIRCLE 27 1.10. THE REAL
MEANING OF THE IMAGINARY ELEMENTS; SYMMETRY, INVERSION AND SIMILARITY 31
1.11. THE CLASSIFICATION OF THE PROJECTIVITIES 40 1.12. THE COMPOSITION
AND THE TRANSFORMATION OF THE PROJECTIVITIES 44 1.13. THE GROUP OF THE
PROJECTIVITIES OF A GIVEN CIRCLE 48 1.14. THE PROJECTIVE MODEL OF THE
LOBACEVSKI S GEOMETRY 52 1.15. BARBILIAN S DISTANCE 55 CHAPTER TWO
BARBILIAN SPACES AND S-BARBILIAN SPACES 2.1. LOGARITHMIC OSCILLATION 57
2.2. CONSTANT GAUSSIAN CURVATURE AND INFLUENCES 66 2.3. S-RIEMANNIAN
MANIFOLDS AS OSCILLANT METRIC SPACES 69 2.4. THE AXIOMATIC THEORY OF
ABSTRACT BARBILIAN SPACES 72 CHAPTER THREE SPECIAL BARBILIAN SPACES AND
THE TZITZEICA CONFIGURATION 3.1. THE TZITZEICA CONFIGURATION ON A SPHERE
81 3.2. THE INTRINSEC POINT OF VIEW 85 3.3. THE CHARACTERISATION OF THE
SPECIAL BARBILIAN SPACES 91 CHAPTER FOUR GEODESIES IN BARBILIAN SPACES
4.1. THE GEODESIES OF OSCILLANT METRIC SPACES 95 4.2. THE AXIOMATIC
THEORY OF APOLLONIU S LINES 101 4.3. THE CONNECTION BETWEEN GEODESIES
AND APOLLONIU S LINES 103 4.4. CONTINOUS BARBILIAN DISTANCE 111 CHAPTER
FIVE LAGRANGEAN STRUCTURES, CONVEX GEOMETRY AND NATURAL BARBILIAN SPACES
5.1. LAGRANGEAN STRUCTURES FOR I-DERIVABLE CURVES 115 III 5.2. THE
GENERALIZED LAGRANGE SPACE INDUCED BY THE POINCARE MODEL OF LOBACEVSKI S
GEOMETRY 122 5.3. CIRCULAR POINTS AND CENTRAL SYMMETRIES 130 5.4.
GK-CIRCLES, SYMMETRIES AND L-BARBILIAN SPACES 134 5.5. THE DIFFERENTIAL
POINT OF VIEW FOR THE AXIOM I 6 143 CHAPTER SIX RIEMANNIAN STRUCTURE FOR
NATURAL BARBILIAN SPACES 6.1. THE LOCAL CONNECTION BETWEEN THE
PSEUDOSPHERE AND 2-DIMENSIONAL NATURAL BARBILIAN SPACES 149 APPENDIX A
154 APPENDIX B 155 INDEX 156 REFERENCES 159 IV
|
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| ctrlnum | (OCoLC)34544391 (DE-599)BVBBV012113325 |
| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012113325 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:21:54Z |
| institution | BVB |
| isbn | 1574850075 |
| language | English |
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| physical | 161 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Hadronic Press |
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| series2 | Series of monographs in advanced mathematics |
| spelling | Boskoff, Wladimir-George Verfasser aut Hyperbolic geometry and barbilian spaces Wladimir-George Boskoff Palm Harbor, FL Hadronic Press 1996 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series of monographs in advanced mathematics Geometry, Hyperbolic GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008202137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boskoff, Wladimir-George Hyperbolic geometry and barbilian spaces Geometry, Hyperbolic |
| title | Hyperbolic geometry and barbilian spaces |
| title_auth | Hyperbolic geometry and barbilian spaces |
| title_exact_search | Hyperbolic geometry and barbilian spaces |
| title_full | Hyperbolic geometry and barbilian spaces Wladimir-George Boskoff |
| title_fullStr | Hyperbolic geometry and barbilian spaces Wladimir-George Boskoff |
| title_full_unstemmed | Hyperbolic geometry and barbilian spaces Wladimir-George Boskoff |
| title_short | Hyperbolic geometry and barbilian spaces |
| title_sort | hyperbolic geometry and barbilian spaces |
| topic | Geometry, Hyperbolic |
| topic_facet | Geometry, Hyperbolic |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008202137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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