Examples of compact Einstein four-manifolds with negative.
Surveys in Differential Geometry: Essays on Einstein Manifolds: Claude Lebrun, McKenzie Wang: 9781571460684: Books - Amazon.ca.
Einstein-Weyl Geometry David M. J. Calderbank and Henrik Pedersen A Weyl manifold is a conformal manifold equipped with a torsion free connec-tion preserving the conformal structure, called a Weyl.
D. Joyce, 'Compact Riemannian manifolds with exceptional holonomy', pages 39-65 in 'Essays on Einstein Manifolds', editors C. LeBrun and M. Wang, Surveys in Differential Geometry VI, International Press, Cambridge, MA, 1999. postscript file.
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Boyer, C. and Galicki, K.: 3-Sasakian manifolds, in: C. LeBrun and M.Wang. (eds), Surveys in Differential Geometry, Vol. VI: Essays on Einstein Manifolds.
Essays. Einstein and Relativity How Einstein discovered the theory of relativity. This is based on a talk I gave at the South Bank Centre. The slides of the talk can be found here. I also made a video where I tried to describe what Einstein's equation of general relativity means. Physics and the Integers PostScript PDF.
Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces.