arXiv subjects

Masoumeh Hosseini

Publications and source records attributed to Masoumeh Hosseini.

7 recordsLinked to original sources

arXiv2024

New Randers metrics defined by the other Randers metrics

In this short article, using a left-invariant Randers metric $F$, we define a new left-invariant Randers metric $\tilde{F}$. We show that $F$ is of Berwald (Douglas) type if and only if $\tilde{F}$ is of Berwald (Douglas) type. In the case of Berwaldian metrics, we give the relation between their flag curvatures. Also, we have studied the relations between their base Riemannian metrics. Finally, as examples, the results are studied in the Heisenberg group and almost Abelian Lie groups.

math.DG↗

arXiv2024

Two-step homogeneous geodesics in some homogeneous Finsler manifolds

A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces $G/H$, known as a two-step homogeneous geodesic, can be expressed of the form $γ(t)=π(\exp(tx)\exp(ty))$, where $x$ and $y$ are elements of the Lie algebra of $G$. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for $(α,β)$ spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two-step Finsler geodesic orbit spaces. Additionally, we present some illustrative examples of these spaces.

math.DG↗

arXiv2022

Conformally related invariant $(α,β)$-metrics on homogeneous spaces

In this paper, we give the flag curvature formula of general $(α,β)$-metrics of Berwald type. We study conformally related $(α,β)$-metrics, especially general $(α,β)$-metrics that are conformally related to invariant $(α,β)$-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an $(α,β)$-metric is given, and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related $(α,β)$-metrics.

math.GM↗

arXiv2021

Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces

In this article, we study Einstein Kropina metrics on Lie groups and homogeneous spaces. We give a method to construct Einstein Kropina metrics on Lie groups. As an example of this method, a family of non-Riemannian Einstein Kropina metrics on the special orthogonal group $SO(n)$ is given. Then, we classify all left invariant Einstein Kropina metrics on simply connected $3$-dimensional real Lie groups. We provide a procedure to build Einstein Kropina metrics on homogeneous spaces. Using this technique, we study invariant Einstein Kropina metrics on spheres. Finally, we show that projective spaces do not admit any homogeneous non-Riemannian Einstein Kropina metrics.

math.DG↗

arXiv2019

Classification of Douglas $(α,β)$-metrics on five dimensional nilpotent Lie groups

In this paper we classify all simply connected five dimensional nilpotent Lie groups which admit $(α,β)$-metrics of Berwald and Douglas type defined by a left invariant Riemannian metric and a left invariant vector field. During this classification we give the geodesic vectors, Levi-Civita connection, curvature tensor, sectional curvature and $S$-curvature.

math.DG↗

arXiv2019

On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spaces

Recently, it is shown that each regular homogeneous Finsler space $M$ admits at least one homogeneous geodesic through any point $o\in M$. The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous $(α,β)$-spaces, specially, homogeneous Kropina spaces. We show that any homogeneous Kropina space admits at least one homogeneous geodesic through any point. It is shown that, under some conditions, the same result is true for any $(α,β)$-homogeneous space. Also, in the case of homogeneous Kropina space of Douglas type, a necessary and sufficient condition for a vector to be a geodesic vector is given. Finally, as an example, homogeneous geodesics of $3$-dimensional non-unimodular real Lie groups equipped with a left invariant Randers metric of Douglas type are investigated.

math.DG↗

arXiv2016

On the left invariant $(α,β)$-metrics on some Lie groups

We give the explicit formulas of the flag curvatures of left invariant Matsumoto and Kropina metrics of Berwald type. We can see these formulas are different from previous results given recently. Using these formulas, we prove that at any point of an arbitrary connected non-commutative nilpotent Lie group, the flag curvature of any left invariant Matsumoto and Kropina metrics of Berwald type admits zero, positive and negative values, this is a generalization of Wolf's theorem. Then we study $(α,β)$-metrics of Berwald type and also Randers metrics of Douglas type on two interesting families of Lie groups considered by Milnor and Kaiser, containing Heisenberg Lie groups. On these spaces, we present some necessary and sufficient conditions for $(α,β)$-metrics to be of Berwald type and also some necessary and sufficient conditions for Randers metrics to be of Douglas type. All left invariant non-Berwaldian Randers metrics of Douglas type are given and the flag curvatures are computed.

math.DG↗