Einstein metrics, projective structures and the SU(∞) Toda equation

1786 - 0091 Projective Einstein Finsler Metrics

In the present paper, we investigate the necessary and sufficient condition of a given Finsler metric to be Einstein. The considered Einstein Finsler metric in the study describes all different kinds of Einstein metrics which are pointwise projective to the given one.

Projective Invariant Metrics for Einstein Spaces

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Einstein - Weyl structures and Bianchi metrics

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kahler ; in the non-exact Einstein-Weyl case with a Bianchi metr...

Einstein–Maxwell–Dilaton metrics from three–dimensional Einstein–Weyl structures

A class of time dependent solutions to (3 + 1) Einstein–Maxwell-dilaton theory with attractive electric force is found from Einstein–Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev–Petviashvili and SU(∞) Toda equations. These solutions are obtained from time–like Kaluza–Klein reductions of (3 + 2) solitons. ∗email [email protected]