Related papers: On contact sub-pseudo-Riemannian isometries

Take a riemanniann nilmanifold, lift its metric on its universal cover. In that way one obtains a metric invariant under the action of some co-compact subgroup. We use it to define metric balls and then study the spectrum of the laplacian…

We study all four-dimensional simply-connected indecomposable non-semisimple pseudo-Riemannian symmetric spaces whose metric has signature (2,2). We present models and compute their isometry groups. We solve the problem of the existence or…

In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for…

Almost Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e. an almost contact B-metric manifold, obtained from a cosymplectic manifold of the considered type by a contact conformal…

A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be…

This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space (other than the octonion hyperbolic plane), and consider the space L(M) of oriented geodesics of M. The space L(M) is…

We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local…

We study the family of vertical projections whose fibers are right cosets of horizontal planes in the Heisenberg group, $\mathbb{H}^n$. We prove lower bounds for Hausdorff dimension distortion of sets under these mappings, with respect to…

We introduce a topological invariant, it a type of a graph-manifold, which takes natural values. For a 4-dimensional graph-manifold, whose type does not exceed two, it is proved that its universal cover is bi-Lipschitz equivalent to a…

We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group $H_{2n + 1}$.…

We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…

We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric…

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extension is Einstein. We exhibit Riemannian extension Osserman…

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…

In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics,…

Let $M$ be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group $G$ acts transitively and isometrically on $M$. In this situation, the metric on $M$ induces a bilinear form…

The left-invariant sub-Lorentzian problem on the Heisenberg group is considered. An optimal synthesis is constructed, the sub-Lorentzian distance and spheres are described.

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and…

We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $…