Related papers: On the left invariant $(\alpha,\beta)$-metrics on …

In this paper, the Cartan tensors of the $(\alpha,\beta)$-norms are investigated in details. Then an equivalence theorem of $(\alpha,\beta)$-norms is proved. As a consequence in Finsler geometry, general $(\alpha,\beta)$-metrics on smooth…

In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…

We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the…

In the context of a connected, simply connected, nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invariant spaces under the left translations associated with the…

We investigate the local metrizability of Finsler spaces with $m$-Kropina metric $F = \alpha^{1+m}\beta^{-m}$, where $\beta$ is a closed null 1-form. We show that such a space is of Berwald type if and only if the (pseudo-)Riemannian metric…

We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there exists a left invariant Riemannian metric and a cyclic…

In this paper we parametrize the symmetry group of the n-dimensional Berwald-Moor metric. Some properties of this Lie group are studied, and its corresponding Lie algebra is computed.

We give a complete classification of homogeneous $(\alpha,\beta)$-metrics with positive flag curvature and vanishing S-curvature.

In this paper, first we derive an explicit formula for the flag curvature of a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce it for naturally reductive homogeneous Finsler…

In this paper, we consider left-invariant para-complex structures on six-dimensional nilpotent Lie groups. A complete list of six-dimensional nilpotent Lie groups that admit para-K\"{a}hler structures is obtained, explicit expressions for…

For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.

In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions…

The Killing form \beta\ of a real (or complex) semisimple Lie group G is a left-invariant pseudo-Riemannian (or, respectively, holomorphic) Einstein metric. Let \Omega\ denote the multiple of its curvature operator, acting on symmetric…

We prove that a complete K\"ahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete K\"ahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly…

In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F. As an application we show…

We define a $\mathbb{Q}$-valued deformation invariant of certain complete Riemann-Finsler manifolds, in particular of complete Riemannian manifolds with non positive sectional curvature. It is proved that every rational number is the value…

This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We…

In this paper angular curvature measures are investigated. Our first result is a complete classification of translation-invariant angular smooth curvature measures on $\mathbb{R}^n$. Subsequently, we use this result to show that the class…

We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-direct extensions of the Heisenberg group are classified,…

We introduce two constructions to obtain left-invariant Ricci-flat pseudo-Riemannian metrics on nilpotent Lie groups, one based on gradings, the other on filtrations, both depending on the combinatorics of the set of weights. As an…