Osserman Manifolds in Semi-Riemannian Geometry

2002
ISBN: 978-3-540-43144-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1777, 170 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 289 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Garcia-Rio, Eduardo

Vazquez-Lorenzo, Ramon

Kupeli, Demir N.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

The Osserman Conditions in Semi-Riemannian Geometry.- The Osserman Conjecture in Riemannian Geometry.- Lorentzian Osserman Manifolds.- Four-Dimensional Semi-Riemannian Osserman Manifolds with Metric Tensors of Signature (2,2).- Semi-Riemannian Osserman Manifolds.- Generalizations and Osserman-Related Conditions.