Related papers: Some isometry groups of Urysohn space

We construct and classify all groups, given by triangular presentations associated to the smallest thick generalized quadrangle, that act simply transitively on the vertices of hyperbolic triangular buildings of the smallest non-trivial…

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

This article is a partial answer to the question of which groups can be represented as isometry groups of formal languages for generalized Levenshtein distances. Namely, it is proved that for any language the modulus of the difference…

We give a construction of the Gurarij space, analogous to Katetov's construction of the Urysohn space. The adaptation of Katetov's technique uses a generalisation of the Arens-Eells enveloping space to metric space with a distinguished…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily…

A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topological group G is g-reversible if every continuous automorphism…

We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: $(\mathbb{Q},+)$, which is the dual of the…

We describe surjective linear isometries and linear isometry groups of a large class of Lipschitz-free spaces that includes e.g. Lipschitz-free spaces over any graph. We define the notion of a Lipschitz-free rigid metric space whose…

We investigate a relations of almost isometric embedding and almost isometry between metric spaces and prove that with respect to these relations: (1) There is a countable universal metric space. (2) There may exist fewer than continuum…

An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for…

We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…

We define the Born group as the group of transformations that leave invariant the line element of Minkowski's spacetime written in terms of Fermi coordinates of a Born congruence. This group depends on three arbitrary functions of a single…

We construct uncountably many finitely generated, pairwise non-isomorphic torsion-free groups, all of which fall into the same quasi-isometry class. This is done by considering Schur covering groups and group cohomology, with the necessary…

We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) "exotic" isometric flow.…

Let $M=G/H$ be a compact connected isotropy irreducible Riemannian homogeneous manifold, where $G$ is a compact Lie group (may be, disconnected) acting on $M$ by isometries. This class includes all compact irreducible Riemannian symmetric…

We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are flat except in dimension 12.

Each Abelian subgroup of the fundamental group of a compact and locally simply connected $d$-dimensional length space with no conjugate points is isomorphic to $\mathbb{Z}^k$ for some $0 \leq k \leq d$. It follows from this and previously…

We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also…