Conformal vector fields on some Finsler manifolds

Abstract

In this paper, we study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R n .

A class of Finsler metrics with conformal radical fields

“…此时, 径向向量场 V x := x 是 F (x, y) := φ(y) 的共 形向量场, 其伸缩系数为常数 c ≡ 1 2 (参见文献 [2]). 近年来, 对 Finsler 流形上的共形向量场的研究得到广泛关注 (参见文献 [1,[3][4][5][6][7][8]). Shen 和 Xia [5] 完全确定了局部射影平坦 Randers 流形上的共形向量场.…”

“…Huang 和 Mo [7] 具体构造了广义 Poincaré 度量上的一个非平凡的共形向量场, 并建立了共形航海问题中的旗曲 率的关系. 最近, Shen 和 Yuan [8] 得到了 R n 上球对称度量的共形向量场具体的表达式.…”

On the geometric structure ofsome statistical manifolds

“…The famous Einstein's relativity theory depends on Riemannian geometry and recently some researchers are interested in extending the relativity theory by using the more general Riemann-Finsler geometry. See [4,7,8,9,18,19] for some references. In 1982, Amari provided a differential geometrical framework for analyzing statistical problmes related to mult-parameter families of distribution and introduced the α-geometry on statistical manifold( [1]).…”

General $(α, β)$ metrics with relatively isotroic mean Landsberg curvature

“…where φ = φ(b 2 , s) is a C ∞ positive function and b = ||β|| α is its norm [8]. It is called general (α, β) metrics.…”

“…Example 1. [8] The Randers metrics and the square metrics are defined by functions φ = φ(b 2 , s) in the following form:…”