Osserman Manifolds in Semi-Riemannian Geometry

✍ Scribed by Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2002
• Tongue: English
• Leaves: 175
• Series: Lecture Notes in Mathematics 1777
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

1. The Osserman Conditions in Semi-Riemannian Geometry....Pages 1-20
   2. The Osserman Conjecture in Riemannian Geometry....Pages 21-37
   3. Lorentzian Osserman Manifolds....Pages 39-61
   4. Four-Dimensional Semi-Riemannian Osserman Manifolds with Metric Tensors of Signature (2,2)....Pages 63-94
   5. Semi-Riemannian Osserman Manifolds....Pages 95-136
   6. Generalizations and Osserman-Related Conditions....Pages 137-156
   References....Pages 157-163
   Index....Pages 165-166
   

✦ Subjects

Differential Geometry; Mathematical and Computational Physics