Semi-Riemannian Maps and Their Applications

1999
ISBN: 978-0-7923-5661-5
Verlag: Springer Netherlands

Buch, Englisch, 198 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1050 g

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.

Kupeli, D. N.

García-Río, Eduardo

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.