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Osserman Manifolds in Semi-Riemannian Geometry

  • Book
  • © 2002

Overview

Authors:
  1. Eduardo García-Río
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  2. Demir N. Kupeli
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  3. Ramón Vázquez-Lorenzo
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1777)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XII
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  2. 1. The Osserman Conditions in Semi-Riemannian Geometry

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 1-20

  3. 2. The Osserman Conjecture in Riemannian Geometry

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 21-37

  4. 3. Lorentzian Osserman Manifolds

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 39-61

  5. 4. Four-Dimensional Semi-Riemannian Osserman Manifolds with Metric Tensors of Signature (2,2)

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 63-94

  6. 5. Semi-Riemannian Osserman Manifolds

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 95-136

  7. 6. Generalizations and Osserman-Related Conditions

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 137-156

  8. References

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 157-163

  9. Index

    • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo
    Pages 165-166

  10. Back Matter

    Pages 167-169
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Keywords

About this book

The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

Bibliographic Information

  • Book Title: Osserman Manifolds in Semi-Riemannian Geometry

  • Authors: Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b83213

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43144-2Published: 25 February 2002

  • eBook ISBN: 978-3-540-45629-2Published: 12 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 170

  • Topics: Differential Geometry, Theoretical, Mathematical and Computational Physics

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