We study the existence of projectable G-invariant Einstein metrics on the total space of G-equivariant fibrations M = G/L → G/K, for a compact connected semisimple Lie group G. We obtain necessary conditions for the existence of such Einstein metrics in terms of appropriate Casimir operators, which is a generalization of the result by Wang and Ziller about Einstein normal metrics. We describe b...

We study the phase space of the spherically symmetric solutions of Einstein-Maxwell-Gauss-Bonnet system nonminimally coupled to a scalar field and prove the existence of solutions with unusual asymptotics in addition to asymptotically flat ones. We also find new dyonic solutions of dilatonic Einstein-Maxwell theory.

The twistor space Z of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in [C-Y]. The purpose of this paper is to compare these two families. In particular we compare the Ricci tensor and the behavior under the Ricci flow of these...

In this paper we prove that the Kähler-Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles GromovHausdorff converge to the complete Kähler-Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total space. We also prove the incompleteness of the Weil-Peterson metric in this case.

Let (M, g) be a compact Einstein manifold with non-empty boundary ∂M . We prove that Killing fields at ∂M extend to Killings fields of (any) (M, g) provided ∂M is (weakly) convex and π1(M,∂M) = {e}. This gives a new proof of the classical infinitesimal rigidity of convex surfaces in Euclidean space and generalizes the result to Einstein metrics of any dimension.

A Riemannian metric is said to be Einstein if the Ricci curvature is a constant multiple of the metric. Given a manifold M , one can ask whether M carries an Einstein metric, and if so, how many. This fundamental question in Riemannian geometry is for the most part unsolved (cf. [Bes]). As a global PDE or a variational problem, the question is intractible. It becomes more manageable in the homo...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional basis space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G : • ...

where Ric(ωKS) is the Ricci form of gKS and LXωKS denotes the Lie derivative of ωKS along a holomorphic vector field X on M . If X = 0, then gKS is a Kähler-Einstein metric with positive scalar curvature. We will show that the second variation of Perelman’s Wfunctional is non-positive in the space of Kähler metrics with 2πc1(M) as Kähler class. Furthermore, if (M, gKS) is a Kähler-Einstein mani...

We give a Hamiltonian formulation of massive spin 2 in arbitrary Einstein space-times. We pay particular attention to Higuchi’s forbidden mass range in deSitter space. Email address: [email protected]

We give a Hamiltonian formulation of massive spin 2 in arbitrary Einstein space-times. We pay particular attention to Higuchi's forbidden mass range in deSitter space. Email address: [email protected]