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

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1431-0821 cessful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals..978-3-540-74120-6978-3-540-74311-8Series ISSN 1431-0821 Series E-ISSN 2512-5257

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Relativity,ield in the absence of matter. This equation was formulated by Einstein in 1915. A brief history of the development of Einstein’s field equation through quotes from early papers can be found in [Mi-Th-Wh] (pp. 431–434).

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Riemannian Functionals,suitable functional, called the action on the configuration space (cf. [Ab-Ma], [Arn]). Hilbert proved ([Hil]) that the equations of general relativity can be recovered from the action (math) (total scalar curvature). His paper contains prophetic ideas about the role played by the diffeomorphism gro

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Ricci Curvature as a Partial Differential Equation,erential operator. In other words, given a metric ., its Ricci curvature . is computed locally in terms of the first and second partial derivatives of .. We will think of . as prescribed and wish to investigate the properties of the metric. Some natural questions that arise are:

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,K?hler-Einstein Metrics and the Calabi Conjecture,r K?hler, or locally homogeneous. On a complex manifold, one often gets K?hler-Einstein metrics by specific techniques. One reason is perhaps, in the K?hler case, the relative autonomy of the Ricci tensor with regard to the metric, once the complex structure is given. The Ricci tensor—or, to be prec

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