Einstein Metrics and Complex Structures.
Einstein metrics and quaternionic Kähler manifolds.
Einstein metrics and smooth structures.
Einstein metrics and stability for flat connections on compact Hermitian manifolds, and a correspondence with Higgs operators in the surface case.
Einstein metrics on a class of five-dimensional homogeneous spaces
We prove that there is exactly one homothety class of invariant Einstein metrics in each space defined below.
Einstein metrics on exotic spheres in dimensions 7, 11 and 15.
Einstein metrics on rational homology 7-spheres
In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2- connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.
Einstein Metrics on solvable groups.
Einstein Spaces Isometrically Diffeomorphic to a Sphere.
Einstein Structures: Existence Versus Uniqueness.
Einstein-Hermitian and anti-Hermitian 4-manifolds
We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.
Einstein-Hermitian connections on principal bundles and stability.
Einstein-like and conformally flat contact metric three-manifolds.
Einstein-like semi-symmetric spaces
One proves that semi-symmetric spaces with a Codazzi or Killing Ricci tensor are locally symmetric. Some applications of this result are given.
Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature.
Einstein-Weyl structures on lightlike hypersurfaces
We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.
Equivariant connected sums of compact self-dual manifolds.
Erratum to: “Smooth metric measure spaces, quasi-Einstein metrics, and tractors”
The original version of the article was published in Central European Journal of Mathematics, 2012, 10(5), 1733–1762, DOI: 10.2478/s11533-012-0091-x. Unfortunately, it contains a typographical error in display of (27). Here we display the correct version of the equations.
Existence and non-existence of homogeneous Einstein metrics.
Existence of metrics with harmonic curvature and non parallel Ricci tensor.