arXiv research

Classifies cosmological Finsler spacetimes, finding viable non-stationary models.

In this paper, we study the long existence problem of non Berwaldian Landsberg spaces using the conformal transformation point of view. Under conformal transformation, the Berwald and Landesberg tensors are calculated in terms of the T-tensor. By giving examples, we show that under conformal transformation, there are L…

In this paper we classify all non-Berwaldian Randers metrics of Douglas type arising from invariant hyper-Hermitian metrics on simply connected four-dimensional real Lie groups. Also, the formulas of the flag curvature are given and it is shown that, in some directions, the flag curvature of the Randers metrics and the…

It is still a long-standing open problem in Finsler geometry, is there any regular Landsberg metric which is not Berwaldian. However, there are non-regular Landsberg metrics which are not Berwladian. The known examples are established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some ex…

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

The nullity distributions of the two curvature tensors \, $\overast{R}$ and $\overast{P}$ of the Chern connection of a Finsler manifold are investigated. The completeness of the nullity foliation associated with the nullity distribution $\N_{R^\ast}$ is proved. Two counterexamples are given: the first shows that $\N_{R…

We describe the $(α,β)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(α,β)$-metrics that satisfy the $σT$-condition $σ_hT^h_{ijk}=0$, where $σ_h=\frac{\partial σ}{\partial x^h}$ and $σ$ is a smooth function on $M$. These classes have already been obtained by Z. Shen and G. S. Asanov in a completely di…

In this paper, we study almost regular Landsberg general $(α,β)$-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general $(α,β)$-metrics under the conditon that $β$ is closed and conformal to $α$. Under this condition, we p…

The paper studies the holonomy of spherically symmetric Finsler metrics.

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

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 cur…