This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometry, a typical process being to 'choose a co-ordinate system such that ...' It is therefore natural to state the axioms in terms of an undefined class of 'allowable' co-ordinate systems, and to deduce the properties of the space from the nature of the transformations of co-ordinates permitted by the axioms. These earlier axioms are found to be adequate for the differential geometry of an open simply connected space, the most elementary theorems of which occupy the greater part of Chapters III-V. The more general axioms, in terms of allowable co-ordinate systems and without restrictions on the connectivity of the space, are given in Chapter IV.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 216 mm
Breite: 140 mm
Dicke: 6 mm
Gewicht
ISBN-13
978-0-521-06674-7 (9780521066747)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Preface; 1. The arithmetic space of n dimensions; 2. Geometries, groups and co-ordinate systems; 3. Allowable co-ordinates; 4. Cells and scalars; 5. Tangent spaces; 6. A set of axioms for differential geometry; 7. Various Geometries; Index of definitions.
