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AuthorGarcรญa-Rรญo, Eduardo. author
TitleOsserman Manifolds in Semi-Riemannian Geometry [electronic resource] / by Eduardo Garcรญa-Rรญo, Demir N. Kupeli, Ramรณn Vรกzquez-Lorenzo
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect tohttp://dx.doi.org/10.1007/b83213
Descript XIV, 170 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Differential geometry Physics Mathematics Differential Geometry Theoretical Mathematical and Computational Physics



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