Related papers: A Users' Guide to Infra-nilmanifolds and Almost-Bi…

In this paper, we study some basic geometric properties of pseudohermitian submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and existence theorems, and some rigidity theorems.

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed…

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…

We determine which non-crystallographic, almost-crystallographic groups of dimension 4 have the $R_\infty$-property. We then calculate the Reidemeister spectra of the 3-dimensional almost-crystallographic groups and the 4-dimensional…

We define a C^1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C^1-close to N. The…

A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these…

In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…

Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly K\"ahler manifolds is provided.

In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…

We study a summability method called almost convergence for bounded measurable functions defined on a locally compact abelian group. We define almost convergence using topologically invariant means and exhibit two different kinds of…

We describe all abelian groups which can appear as the fundamental groups of closed symplectically aspherical manifolds. The proofs use the theory of symplectic Lefschetz fibrations.

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…

Three-dimensional almost contact B-metric manifolds are constructed by a three-parametric family of Lie groups. It is established the class of the investigated manifolds which has an important geometrical interpretation. It is determined…

The authors investigate the structure of quasi-o-minimal groups. Among other results, they show that quasi-o-minimal groups are abelian, that quasi-o-minimal densely ordered archimedian groups are divisible, and that every divisible…

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…

Using computations in the bidual of $\mathbb{B}(L^2M)$ we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of…

Let $n\geq 3$. In this paper we show that for any finite abelian subgroup $G$ of $S_n$ the crystallographic group $B_n/[P_n,P_n]$ has Bieberbach subgroups $\Gamma_{G}$ with holonomy group $G$. Using this approach we obtain an explicit…

For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.