Related papers: Normal homogeneous Finsler spaces

We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…

Two special Finsler spaces have been introduced and investigated, namely $R^h$-recurrent Finsler space and consircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor…

If a graph submanifold $(x,f(x))$ of a Riemannian warped product space $(M^m\times_{e^{\psi}}N^n,\tilde{g}=g+e^{2\psi}h)$ is immersed with parallel mean curvature $H$, then we obtain a Heinz type estimation of the mean curvature. Namely, on…

We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

In this paper we develop new methods of study of generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres. We prove that for any…

A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of…

A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the same distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous if for any two points $x_1, x_2\in M$ there is a Clifford-Wolf…

Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group.…

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent…

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n>2. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then…

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler…

We describe the structure of $d$-dimensional homogeneous Lorentzian $G$-manifolds $M=G/H$ of a semisimple Lie group $G$. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group $G$ acts properly, that is the…

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

The aim of this paper is to to show the admissibility of some class of Frechet spaces (see Definition 2.3). In particular, this generalizes the main results of [3]. As an application, we show the admissibility of a large class modular…

We classify the metric spaces that can be approximated by finite homogeneous ones.

In this note we complete a study of globally homogeneous Riemannian quotients $\Gamma\backslash (M,ds^2)$ in positive curvature. Specifically, $M$ is a homogeneous space $G/H$ that admits a $G$-invariant Riemannian metric of strictly…

To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…

An $(\alpha,\beta)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $\alpha$ and $1$-form $\beta$ on the manifold $M$. In this paper, we classify $n$-dimensional…

We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. We show that…