Titlebook: Einstein Manifolds; Arthur L. Besse Book 1987 Springer-Verlag Berlin Heidelberg 1987 Einstein.Manifolds.Riemannian geometry.Submersion.Top

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Homogeneous Riemannian Manifolds,In this chapter, we sketch the general theory of homogeneous Riemannian manifolds and we use it to give some examples of (homogeneous) Einstein manifolds. Up to now, the general classification of homogeneous Einstein manifolds is not known even in the compact case. In particular, the following question is still an open problem.

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Riemannian Submersions,The notion of . (see 1.70) has been intensively studied since the very beginning of Riemannian geometry. Indeed the first Riemannian manifolds to be studied were surfaces imbedded in R.. As a consequence, the differential geometry of Riemannian immersions is well known and available in many textbooks (see for example [Ko-No 1, 2], [Spi]).

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Arthur L. BesseIncludes supplementary material:

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https://doi.org/10.1007/978-3-540-74311-8Einstein; Manifolds; Riemannian geometry; Submersion; Topology; Volume; curvature; equation; function; geomet

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978-3-540-74120-6Springer-Verlag Berlin Heidelberg 1987

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Geburtshilfliche Operationslehref an infinity of small pieces of Euclidean spaces). In modern language, a Riemannian manifold (.) consists of the following data: a compact .. manifold . and a metric tensor field . which is a positive definite bilinear symmetric differential form on .. In other words, we associate with every point