Orthogonality and Spacetime Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1987
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book examines the geometrical notion of orthogonality, and shows how to use it as the primitive concept on which to base a metric structure in affine geometry. The subject has a long history, and an extensive literature, but whatever novelty there may be in the study presented here comes from its focus on geometries having lines that are self-orthogonal, or even singular (orthogonal to all lines). The most significant examples concern four-dimensional special-relativistic spacetime (Minkowskian geometry), and its various sub-geometries, and these will be prominent throughout. But the project is intended as an exercise in the foundations of geometry that does not presume a knowledge of physics, and so, in order to provide the appropriate intuitive background, an initial chapter has been included that gives a description of the different types of line (timelike, spacelike, lightlike) that occur in spacetime, and the physical meaning of the orthogonality relations that hold between them. The coordinatisation of affine spaces makes use of constructions from projective geometry, including standard results about the matrix represent ability of certain projective transformations (involutions, polarities). I have tried to make the work sufficiently selfcontained that it may be used as the basis for a course at the advanced undergraduate level, assuming only an elementary knowledge of linear and abstract algebra |
| Beschreibung: | 1 Online-Ressource (X, 194 p) |
| ISBN: | 9781468463453 9780387965192 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4684-6345-3 |
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Datensatz im Suchindex
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| author | Goldblatt, Robert |
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| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-6345-3 |
| format | Electronic eBook |
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| isbn | 9781468463453 9780387965192 |
| issn | 0172-5939 |
| language | English |
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| spelling | Goldblatt, Robert Verfasser aut Orthogonality and Spacetime Geometry by Robert Goldblatt New York, NY Springer US 1987 1 Online-Ressource (X, 194 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 This book examines the geometrical notion of orthogonality, and shows how to use it as the primitive concept on which to base a metric structure in affine geometry. The subject has a long history, and an extensive literature, but whatever novelty there may be in the study presented here comes from its focus on geometries having lines that are self-orthogonal, or even singular (orthogonal to all lines). The most significant examples concern four-dimensional special-relativistic spacetime (Minkowskian geometry), and its various sub-geometries, and these will be prominent throughout. But the project is intended as an exercise in the foundations of geometry that does not presume a knowledge of physics, and so, in order to provide the appropriate intuitive background, an initial chapter has been included that gives a description of the different types of line (timelike, spacelike, lightlike) that occur in spacetime, and the physical meaning of the orthogonality relations that hold between them. The coordinatisation of affine spaces makes use of constructions from projective geometry, including standard results about the matrix represent ability of certain projective transformations (involutions, polarities). I have tried to make the work sufficiently selfcontained that it may be used as the basis for a course at the advanced undergraduate level, assuming only an elementary knowledge of linear and abstract algebra Mathematics Geometry Mathematik Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Affine Geometrie (DE-588)4141566-8 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf Affine Geometrie (DE-588)4141566-8 s Raum-Zeit (DE-588)4302626-6 s 1\p DE-604 Orthogonale Funktionen (DE-588)4475233-7 s 2\p DE-604 https://doi.org/10.1007/978-1-4684-6345-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldblatt, Robert Orthogonality and Spacetime Geometry Mathematics Geometry Mathematik Raum-Zeit (DE-588)4302626-6 gnd Affine Geometrie (DE-588)4141566-8 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| subject_GND | (DE-588)4302626-6 (DE-588)4141566-8 (DE-588)4475233-7 |
| title | Orthogonality and Spacetime Geometry |
| title_auth | Orthogonality and Spacetime Geometry |
| title_exact_search | Orthogonality and Spacetime Geometry |
| title_full | Orthogonality and Spacetime Geometry by Robert Goldblatt |
| title_fullStr | Orthogonality and Spacetime Geometry by Robert Goldblatt |
| title_full_unstemmed | Orthogonality and Spacetime Geometry by Robert Goldblatt |
| title_short | Orthogonality and Spacetime Geometry |
| title_sort | orthogonality and spacetime geometry |
| topic | Mathematics Geometry Mathematik Raum-Zeit (DE-588)4302626-6 gnd Affine Geometrie (DE-588)4141566-8 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| topic_facet | Mathematics Geometry Mathematik Raum-Zeit Affine Geometrie Orthogonale Funktionen |
| url | https://doi.org/10.1007/978-1-4684-6345-3 |
| work_keys_str_mv | AT goldblattrobert orthogonalityandspacetimegeometry |