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Orthogonality and Spacetime Geometry (Paperback, Softcover reprint of the original 1st ed. 1987)
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Orthogonality and Spacetime Geometry (Paperback, Softcover reprint of the original 1st ed. 1987)
Series: Universitext
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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 hav ing 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 var ious sub-geometries, and these will be
prominent throughout. But the project is intended as an exercise in
the foundations of geome try 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 ma trix
represent ability of certain projective transformations (involu
tions, polarities). I have tried to make the work sufficiently self
contained that it may be used as the basis for a course at the ad
vanced undergraduate level, assuming only an elementary knowledge
of linear and abstract algebra."
General
Imprint: |
Springer-Verlag New York
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Country of origin: |
United States |
Series: |
Universitext |
Release date: |
May 1987 |
First published: |
1987 |
Authors: |
Robert Goldblatt
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Dimensions: |
235 x 155 x 10mm (L x W x T) |
Format: |
Paperback
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Pages: |
194 |
Edition: |
Softcover reprint of the original 1st ed. 1987 |
ISBN-13: |
978-0-387-96519-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
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LSN: |
0-387-96519-X |
Barcode: |
9780387965192 |
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