The geometry of curvature homogeneous pseudo-Riemannian manifolds / Peter B. Gilkey.
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Includes bibliographical references (pages 361-372) and index.
Print version record.
Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov?Tsankov?Videv theory.
The geometry of the Riemann curvature tensor -- Curvature homogeneous generalized plane wave manifolds -- Other pseudo-Riemannian manifolds -- The curvature tensor -- Complex Osserman algebraic curvature tensors -- Stanilov-Tsankov theory.
English.