Metric planes and metric vector spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York (u.a.)
Wiley
1979
|
| Series: | A Wiley-Interscience publication.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 209 S. graph. Darst. |
| ISBN: | 0471049018 |
Staff View
MARC
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| 300 | |a XI, 209 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804116721535025152 |
|---|---|
| adam_text | CONTENTS
Chapter 1. Metric Vector Spaces 1
1. Basic Definitions 1
2. Isotropic Subspaces and Witt-Index 3
3. Representation in a Basis 5
4. Reflections and the Orthogonal Group 6
Chapter 2. Incidence Structures 9
1. Ternary Equivalence Relations 9
2. Incidence Structures 10
3. Projective Incidence Structures and Substructures 12
4. Projective and Affine Incidence Structures Over a Field 14
5. Incidence Structures Over a Metric Vector Space 15
Chapter 3. Metric Concepts 18
1. Classical Euclidean and Non-Euclidean Planes 18
2. Incidence Structures with Orthogonality 21
3. Metric Incidence Structure Over a Metric Vector Space 22
4. Incidence Structures with Reflections 24
5. Complete Metric Planes 24
6. Metric Plane Over a Metric Vector Space 30
7. Definition of Euclidean and Non-Euclidean Coordinate
Planes 33
Chapter 4. S-Groups and S-Group Planes 35
1. Definition 35
2. Group Plane of an S-Group 35
3. Elementary Properties 37
4. Reflections and Motions 38
5. Some Metric Configuration Theorems for S-Group Planes 39
6. The Center of an S-Group 41
7. S-Group Planes and S-Planes 42
IX
x CONTENTS
Chapter 5. S-Group Planes with A-Connected Points 47
1. The Reduction Theorem 47
2. The Theorem of the Set of Perpendiculars to a Line 49
3. The Mapping o-qAB (Gegenpunktpaarung) 54
4. Dropping a Perpendicular to a Given Line Through a
Given Point 58
5. Theorem of Pappus-Brianchon 60
6. Theorem of Desargues 62
7. Embeddable S-Group Planes 66
8. Quadratic Form of S-Group Planes with Completely
Connected Points 66
Chapter 6. Complete S-Group Planes 77
1. Main Theorems on Complete S-Group Planes 77
2. 2-A-Connected Points in an Arbitrary S-Group Plane 78
3. The Five Types of Complete S-Group Planes 83
4. The Elliptic Planes 89
5. The Euclidean Planes 91
6. The Strubecker Planes 95
7. The Hyperbolic-Metric Planes 104
8. The Minkowskian Planes 115
9. Main Theorem on Complete Metric Planes 130
10. Polar Points in Complete S-Group Planes 132
11. Characteristic of a Complete S-Group Plane 135
Chapter 7. S-Group Planes with Completely Connected Points 140
1. Definition of S-Group Planes with Completely Connected
Points and the Main Theorem 140
2. Proper Points on a Line 141
3. Germs of Perspective Collineations 144
4. The Ideal Incidence Structure of an S-Group Plane with
Completely Connected Points 152
5. Remarks 155
6. Normalizer Planes 157
Chapter 8. Finite S-Groups 162
1. Elementary Remarks on Finite S-Groups 162
2. Finite S-Group Planes with Completely Connected Points 165
3. Finite S-Group Planes with 1-A-Connected Points 173
4. Remarks 185
CONTENTS xi
Appendix: Affine and Projective Planes 187
1. AiEne Planes 187
2. Projective Planes 189
3. Projective Closure of an Affine Plane 192
4. Affine Spaces 193
5. Perspective Collineations of a Projective Plane 194
6. Collineations Induced by Linear Mappings 195
7. Projective Reflections 195
8. Projective Reflection Groups 196
9. Definition of Some Classical Groups 201
Bibliography 203
Index 207
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 515 - Analysis |
| dewey-raw | 516.9 515/.73 |
| dewey-search | 516.9 515/.73 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002263910 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:01Z |
| institution | BVB |
| isbn | 0471049018 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001487766 |
| oclc_num | 4497215 |
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| physical | XI, 209 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication. |
| spelling | Lingenberg, Rolf Verfasser aut Metric planes and metric vector spaces New York (u.a.) Wiley 1979 XI, 209 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication. Geometry, Non-Euclidean Geometry, Plane Vector spaces Vektorraum (DE-588)4130622-3 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf S-Gruppe (DE-588)4181126-4 gnd rswk-swf S-Gruppe (DE-588)4181126-4 s DE-604 Vektorraum (DE-588)4130622-3 s Metrischer Raum (DE-588)4169745-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lingenberg, Rolf Metric planes and metric vector spaces Geometry, Non-Euclidean Geometry, Plane Vector spaces Vektorraum (DE-588)4130622-3 gnd Metrischer Raum (DE-588)4169745-5 gnd S-Gruppe (DE-588)4181126-4 gnd |
| subject_GND | (DE-588)4130622-3 (DE-588)4169745-5 (DE-588)4181126-4 |
| title | Metric planes and metric vector spaces |
| title_auth | Metric planes and metric vector spaces |
| title_exact_search | Metric planes and metric vector spaces |
| title_full | Metric planes and metric vector spaces |
| title_fullStr | Metric planes and metric vector spaces |
| title_full_unstemmed | Metric planes and metric vector spaces |
| title_short | Metric planes and metric vector spaces |
| title_sort | metric planes and metric vector spaces |
| topic | Geometry, Non-Euclidean Geometry, Plane Vector spaces Vektorraum (DE-588)4130622-3 gnd Metrischer Raum (DE-588)4169745-5 gnd S-Gruppe (DE-588)4181126-4 gnd |
| topic_facet | Geometry, Non-Euclidean Geometry, Plane Vector spaces Vektorraum Metrischer Raum S-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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