García-Río / Kupeli Semi-Riemannian Maps and Their Applications

1999
ISBN: 978-94-017-2979-6
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 475, 198 Seiten, eBook

Reihe: Mathematics and Its Applications

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.
This volume will be of interest to mathematicians and physicists whose work involves differential geometry, global analysis, or relativity and gravitation.

Zielgruppe

Research

Autoren/Hrsg.

García-Río, Eduardo

Kupeli, D.N.

Inhaltsverzeichnis

Preface. 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. B. Riemannian and Lorentzian Geometry. Bibliography. Index.