ﻻ يوجد ملخص باللغة العربية
In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(alpha,beta)$-space of non-Randers type in dimension $nge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fields are not necessarily homothetic.
In this paper, we characterize conformal vector fields of any (regular or singular) $(alpha,beta)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(alpha,beta)$-spaces satisfying certain geometric conditions.
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(alpha,beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to st
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 $(alpha,beta)$-manifolds (non-Rander
In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=alpha^2/beta$ with constant curvature $K$ and $|beta|_{alpha}=1$ is projectively flat if and only if $F$ is locally Minkowskian.
In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$ with ${rm