Related papers: A class of nonsymmetric harmonic Riemannian spaces

The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

We classify four-dimensional connected simply-connected indecomposable Lorentzian symmetric spaces $M$ with connected nontrivial isotropy group furnishing solutions of the Einstein-Yang-Mills equations. Those solutions with respect to some…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

In this article we classify totally geodesic submanifolds in arbitrary products of rank one symmetric spaces. Furthermore, we give infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces with…

In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can…

We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.

In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class…

For $n\ge 3$, let $\Omega$ be a bounded domain in $R^n$ and $N$ be a compact Riemannian manifold in $R^L$ without boundary. Suppose that $u_n\in W^{1,n}(\Omega,N)$ are the Palais-Smale sequences of the Dirichlet $n$-energy functional and…

On any closed Riemannian manifold of dimension greater than $7$, we construct examples of background physical coefficients for which the Einstein-Lichnerowicz equation possesses a non-compact set of positive solutions. This yields in…

Classical harmonic analysis says that the spaces of homogeneous harmonic polynomials (solutions of Laplace equation) are irreducible modules of the corresponding orthogonal Lie group (algebra) and the whole polynomial algebra is a free…

In this article we consider asymptotically harmonic manifolds which are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature $h$. We prove the following…

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action…

Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…

We consider a class of fully non-linear parabolic equations on compact Hermitian manifolds involving symmetric functions of partial Laplacians. Under fairly general assumptions, we show the long time existence and convergence of solutions.…

Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric…

We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…

Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…