The Foundations of Differential Geometry

Erscheinungsjahr 2008
ISBN: 978-0-521-06674-7
Verlag: Cambridge University Press

Buch, Englisch, 108 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 148 g

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.

Autoren/Hrsg.

Veblen, Oswald

Whitehead, J. H. C.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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.