The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the SL(2, R) principal chiral model with certain ‘source’ terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as exp...

The aim of this paper is to study a contact Riemannian submersion ? : M B between almost metric manifolds such that its total space admits an ??Ricci soliton. Here, we obtain some necessary conditions for which any fiber and the manifold are soliton, Ricci generalized quasi-Einstein, ??Einstein or Einstein. Finally, equipped with torqued vector field give characterizations ?.

We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M6, with four-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, ...

In this note, we announce some results showing unexpected similarities between the moduli spaces of constant curvature metrics on 2-manifolds (the Riemann moduli space) and moduli spaces of Einstein metrics on 4manifolds. Let J? denote the moduli space of Einstein metrics of volume 1 on a compact, orientable 4-manifold M. If J£\ denotes the space of smooth Riemannian metrics of volume 1 on M, e...

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial progress towards the understanding of Einstein nilradicals, there is still a la...

We verify the extension to zero section of momentum construction Kaehler-Einstein metrics and Kaehler-Ricci solitons on total space Y positive rational powers canonical line bundle toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. More precisely, we show that extended metric along has an expression which can be Y, restricts associated unit circle as a transversely (Sasakian ...

Abstract We continue our study of the mixed Einstein–Hilbert action as a functional pseudo-Riemannian metric and linear connection. Its geometrical part is total scalar curvature on smooth manifold endowed with distribution or foliation. develop variational formulas for quantities extrinsic geometry metric-affine space use them to derive Euler–Lagrange equations (which in case space-time are an...

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.