Invariant Einstein metrics on three-locally-symmetric spaces

Projective Invariant Metrics for Einstein Spaces

Some New Homogeneous Einstein Metrics on Symmetric Spaces

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with rank(M) > 1, not isometric to a compact Lie group. Whenever there exists a closed proper subgroup G of Isom(M) acting transitively on M we nd all G-homogeneous (non-symmetric) Einstein metrics on M .

Invariant Metrics on G-spaces

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

Homogeneous Einstein–weyl Structures on Symmetric Spaces

In this paper we examine homogeneous Einstein–Weyl structures and classify them on compact irreducible symmetric spaces. We find that the invariant Einstein–Weyl equation is very restrictive: Einstein–Weyl structures occur only on those spaces for which the isotropy representation has a trivial component, for example, the total space of a circle bundle.

Moduli spaces of Einstein metrics

We discuss the space of Einstein metrics, up to diffeomorphism, on a compact manifold. In particular we mention some heuristics on its dimension and some theorems on its compactness.