Related papers: Compact locally homogeneous manifolds with paralle…

In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two…

Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes…

Let $E$ be a Riesz space and let $E^{\sim}$ denote its order dual. The orthomorphisms $Orth(E)$ on $E,$ and the ideal center $Z(E)$ of $E,$ are naturally embedded in $Orth(E^{\sim})$ and $Z(E^{\sim})$ respectively. We construct two unital…

On any manifold, any non-degenerate symmetric 2-form (metric) and any skew-symmetric (differential) form W can be reduced to a canonical form at any point, but not in any neighborhood: the respective obstructions being the Riemannian tensor…

The objective of the paper is to investigate a sequential study of different generalizations of semisymmetric and pseudosymmetric manifolds with their proper existence by several spacetimes. In the literature of differential geometry, there…

We show that on any Riemannian manifold with H\"older continuous metric tensor, there exists a $p$-harmonic coordinate system near any point. When $p = n$ this leads to a useful gauge condition for regularity results in conformal geometry.…

In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient…

We consider non-Kaehler compact complex manifolds which are homogeneous under the action of a compact Lie group of biholomorphisms and we investigate the existence of special (invariant) Hermitian metrics on these spaces. We focus on a…

A smooth curve on a homogeneous manifold $G/H$ is called a Riemannian equigeo-desic if it is a homogeneous geodesic for any $G$-invariant Riemannian metric. The homogeneous manifold $G/H$ is called Riemannian equigeodesic, if for any $x\in…

A method, due to \'Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant…

In this paper we investigate $m$-dimensional complete minimal submanifolds in Euclidean spheres with index of relative nullity at least $m-2$ at any point. These are austere submanifolds in the sense of Harvey and Lawson \cite{harvey} and…

"Diagonal" spatially inhomogeneous (SI) models are introduced under the assumption of the existence of (proper) intrinsic symmetries and can be seen, in some sense, complementary to the Szekeres models. The structure of this class of…

The paper investigates two invariants for totally disconnected locally compact groups: the number of ends and the rational discrete cohomological dimension. For such a compactly generated group $G$ it is shown that its number of ends can be…

We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to M in…

Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal…

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced…

For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application, we show in…

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy"…

We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting…