of the Dissertation Ricci-Flat Anti-Self-Dual Asymptotically Locally Euclidean 4-Manifolds by Evan Patrick Wright Doctor of Philosophy in Mathematics Stony Brook University 2013 A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or a cyclic quo...

Using symmetry arguments only, we show that every spacetime with mirror-symmetric spatial sections is necessarily conformally flat. The general form of the Ricci tensor of such spacetimes is also determined. 1. Introduction. It is well known that the curvature tensor of any four-dimensional differentiable manifold has only 20 algebraically independent components. Ten out of these 20 components ...

We construct examples of compact homogeneous Riemannian manifolds admitting an invariant Bismut connection that is Ricci flat and non-flat, proving in this way the generalized Alekseevsky–Kimelfeld theorem does not hold. The classification spaces dimension $5$ also provided. Moreover, we investigate with non-trivial third Betti number, point out other possible ways to manifolds. Finally, since ...

We prove the non-existence of Levi flat compact real hypersurfaces without boundary in CPn, n > 1, with non-negative totally real Ricci curvature.

Gravitational instantons, solutions to the euclidean Einstein equations, with topology R3XS1 arise naturally in any discussion of finite temperature quantum gravity. This Letter shows that all such instantons (irrespective of their interior behaviour) must have the same asymptotic structure as the Schwarzschild instanton. Using this, it can be shown that if the Ricci tensor of the manifold is n...