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Semi-Riemannian maps and their applications

Author: Eduardo García-Río; Demir N Kupeli
Publisher: Dordrecht : Springer, ©1999.
Series: Mathematics and its applications (Kluwer Academic Publishers), 475.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Eduardo García-Río; Demir N Kupeli
ISBN: 9789401729796 9401729794 904815202X 9789048152025
OCLC Number: 859588796
Description: 1 online resource (x, 198 pages).
Contents: 1 Linear Algebra of Indefinite Inner Product Spaces --
2 Semi-Riemannian Manifolds --
3 Second Fundamental Form of a Map --
4 Semi-Riemannian Maps --
5 Semi-Riemannian Transversal Maps --
6 Semi-Riemannian Eikonal Equations and The Semi-Riemannian Regular Interval Theorem --
7 Applications To Splitting Theorems --
A Submanifolds of Semi-Riemannian Manifolds --
A.1 Semi-Riemannian Submanifolds --
A.2 Degenerate Submanifolds --
B Riemannian and Lorentzian Geometry --
B.1 Riemannian Geometry --
B.2 Lorentzian Geometry.
Series Title: Mathematics and its applications (Kluwer Academic Publishers), 475.
Responsibility: Eduardo García-Río and Demir N. Kupeli.

Abstract:

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.

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