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Osserman manifolds in semi-Riemannian geometry. (English) Zbl 1005.53040

Lecture Notes in Mathematics. 1777. Berlin: Springer. xii, 166 p. (2002).
The study of Osserman manifolds goes back to the initial works of Osserman and Sarnak during 1984 followed by Chi (1988), Gilkey (1994) and several others, including a series of papers by the authors of the present book. Osserman manifolds play a significant role in the study of curvature and the metric tensors of Riemannian and semi-Riemannian manifolds and the geometry of affine manifolds.
The objective of this book is to present an up-to-date information on the use of Osserman condition in Riemannian, Lorentzian, general semi-Riemannian and affine geometries. All these topics are discussed in six chapters.
Each chapter contains its preliminaries which enables the reader to understand its contents without reading any other chapter. Overall it is a well written book and is easy to read.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
53C80 Applications of global differential geometry to the sciences
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