Semi-Riemannian Maps and Their Applications

ISBN-13: 9789048152025 / Angielski / Miękka / 2010 / 198 str.

Eduardo García-Río;D.N. Kupeli

Opis

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.

Spis treści

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.