Osserman Manifolds in Semi-Riemannian Geometry

Download or read book Osserman Manifolds in Semi-Riemannian Geometry written by Eduardo Garcia-Rio and published by Springer. This book was released on 2004-10-12 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.