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Semi-Riemannian Maps and Their Applications

  • Book
  • © 1999

Overview

Authors:
  1. Eduardo García-Río

    1. University of Santiago de Compostela, Santiago, Spain

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    You can also search for this author in PubMed   Google Scholar

  2. Demir N. Kupeli

    1. Middle East Technical University, Ankara, Turkey

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 475)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Linear Algebra of Indefinite Inner Product Spaces

    • Eduardo García-Río, Demir N. Kupeli
    Pages 1-18

  3. Semi-Riemannian Manifolds

    • Eduardo García-Río, Demir N. Kupeli
    Pages 19-57

  4. Second Fundamental Form of a Map

    • Eduardo García-Río, Demir N. Kupeli
    Pages 59-82

  5. Semi-Riemannian Maps

    • Eduardo García-Río, Demir N. Kupeli
    Pages 83-100

  6. Semi-Riemannian Transversal Maps

    • Eduardo García-Río, Demir N. Kupeli
    Pages 101-115

  7. Semi-Riemannian Eikonal Equations and The Semi-Riemannian Regular Interval Theorem

    • Eduardo García-Río, Demir N. Kupeli
    Pages 117-141

  8. Applications To Splitting Theorems

    • Eduardo García-Río, Demir N. Kupeli
    Pages 143-162

  9. Back Matter

    Pages 163-198
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Keywords

About this book

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.

Authors and Affiliations

  • University of Santiago de Compostela, Santiago, Spain

    Eduardo García-Río

  • Middle East Technical University, Ankara, Turkey

    Demir N. Kupeli

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