Orthogonality and Spacetime Geometry

Robert Goldblatt

ISBN 10: 038796519X / ISBN 13: 9780387965192

Verlag: Springer New York, Springer US, 1987

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9780387965192

Bibliografische Details

• Titel: Orthogonality and Spacetime Geometry
• Verlag: Springer New York, Springer US
• Erscheinungsjahr: 1987
• Sprache: Englisch
• ISBN-10: 038796519X
• ISBN-13: 9780387965192
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 12 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 12 mm
• Gewicht: 318 Gramm

Über diesen Titel

Inhaltsangabe

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.