Osserman Manifolds in Semi-Riemannian Geometry
García-Río, Eduardo.
Osserman Manifolds in Semi-Riemannian Geometry [electronic resource] / by Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo. - XIV, 170 p. online resource. - Lecture Notes in Mathematics, 1777 0075-8434 ; . - Lecture Notes in Mathematics, 1777 .
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.
9783540456292
10.1007/b83213 doi
Global differential geometry.
Differential Geometry.
Theoretical, Mathematical and Computational Physics.
QA641-670
516.36
Osserman Manifolds in Semi-Riemannian Geometry [electronic resource] / by Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo. - XIV, 170 p. online resource. - Lecture Notes in Mathematics, 1777 0075-8434 ; . - Lecture Notes in Mathematics, 1777 .
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.
9783540456292
10.1007/b83213 doi
Global differential geometry.
Differential Geometry.
Theoretical, Mathematical and Computational Physics.
QA641-670
516.36