Osserman Manifolds in Semi-Riemannian Geometry [electronic resource] / by Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo.

By: García-Río, Eduardo [author.]Contributor(s): Kupeli, Demir N [author.] | Vázquez-Lorenzo, Ramón [author.] | SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1777Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002Description: XIV, 170 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540456292Subject(s): Mathematics | Global differential geometry | Mathematical physics | Mathematics | Differential Geometry | Mathematical and Computational PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 516.36 LOC classification: QA641-670Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
Item type: E-BOOKS
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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.

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.

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