A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties. Here, a class of such maps called semi-Riemannian maps is introduced. The main purpose of this book is to present results in semi-Riemannian geometry obtained by the existence of such a map between semi-Riemannian manifolds, as well as to encourage the reader to explore these maps.
The first three chapters are devoted to the development of fundamental concepts and formulas in semi-Riemannian geometry which are used throughout the work. In Chapters 4 and 5 semi-Riemannian maps and such maps with respect to a semi-Riemannian foliation are studied. Chapter 6 studies the maps from a semi-Riemannian manifold to 1-dimensional semi- Euclidean space. In Chapter 7 some splitting theorems are obtained by using the existence of a semi-Riemannian map.
Audience: This volume will be of interest to mathematicians and physicists whose work involves differential geometry, global analysis, or relativity and gravitation.
|Linear Algebra of Indefinite Inner Product Spaces||p. 1|
|Semi-Riemannian Manifolds||p. 19|
|Second Fundamental Form of a Map||p. 59|
|Semi-Riemannian Maps||p. 83|
|Semi-Riemannian Transversal Maps||p. 101|
|Semi-Riemannian Eikonal Equations and The Semi-Riemannian Regular Interval Theorem||p. 117|
|Applications To Splitting Theorems||p. 143|
|Submanifolds of Semi-Riemannian Manifolds||p. 163|
|Riemannian and Lorentzian Geometry||p. 181|
|Table of Contents provided by Blackwell. All Rights Reserved.|
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Number Of Pages: 198
Published: 1st June 1999
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15 x 2.54
Weight (kg): 0.5