Related papers: Locally Homogeneous Non-gradient Quasi-Einstein 3-…

In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition.…

Let $M$ be a pseudo-Riemannian spin manifold of dimension $n$ and signature $s$ and denote by $N$ the rank of the real spinor bundle. We prove that $M$ is locally homogeneous if it admits more than ${3/4}N$ independent Killing spinors with…

Let $G/H$ be a connected, simply connected homogeneous space of a compact Lie group $G$. We study $G$-invariant quasi-Einstein metrics on the cohomogeneity one manifold $G/H\times (0,1)$ imposing the so-called monotypic condition on $G/H$.…

The paper investigates the (non)existence of compact quotients, by a discrete subgroup, of the homogeneous almost-complex strongly-pseudoconvex manifolds disconvered and classified by Gaussier-Sukhov and K.-H. Lee.

We give a classification, up to local isomorphisms, of semi-simple Lie groups without compact factors that can act faithfully and conformally on a compact Lorentz manifold of dimension greater than or equal to $3$.

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics $g$ on $G = \mathrm{SU}(2) \times \mathrm{SU}(2) = S^3 \times…

We study homogeneous Einstein metrics on indecomposable non-K\"ahlerian C-spaces, i.e. even-dimensional torus bundles $M=G/H$ with $\mathsf{rank} G>\mathsf{rank} H$ over flag manifolds $F=G/K$ of a compact simple Lie group $G$. Based on the…

Let K be a simple and simply connected compact Lie group. We call a (twisted) quasi-Hamiltonian K-manifold M a quasi-Hamiltonian model space if it is multiplicity free and its momentum map is surjective. We explicitly identify the subgroups…

We deal with rigidity results for compact gradient Einstein-type manifolds with nonempty boundaries. As a result, we obtain new characterizations for hemispheres and geodesic balls in simply connected space forms. In dimensions three and…

A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie group structure and $c$ is the conformal structure defined by a left-invariant metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie…

We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics…

We prove that the existence of a positively defined, invariant Einstein metric $m$ on a connected homogeneous space $G/H$ of a compact Lie group $G$ is the consequence of non-contractibility of some compact set $C=X_{G,H}^{\Sigma}$ (B\"ohm…

This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…

We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds…

A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient…

For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved…

Let (M, g) be a compact Einstein manifold with non-empty boundary. We prove that Killing fields at the boundary extend to Killing fields of any (M, g) provided the boundary is weakly convex and a simple condition on the fundamental group…

Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we…

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We…

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $\rho$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to…