Isometries, submetries and distance coordinates on Finsler manifolds

On the Lie group structure of pseudo-Finsler isometries

Using an extension to isometries of the associated Sasaki structure, we establish a Lie transformation group structure for the set of isometries of a pseudo-Finsler conical metric.

On submaximal dimension of the group of almost isometries of Finsler metrics

We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $\frac{n^2 -n}{2} +1$ for $n= dim(M)\ne 4 $ and $\frac{n^2 -n}{2} +2 =8$ for $n=4$. If a Finsler metric has the group of almost isometries of dimension greater than $\frac{n^2 -n}{2} +1$, then the Finsler metric is Randers, i.e., $F(x,y)= \sqrt{g_x(y,y)} + τ(y)$. Moreover, if $n\ne 4$, the Riemannian metric $g$ has constant sectional curvature and, if in addition $n\ne 2$, the 1-form $τ$ is closed, so (locally) the metric admits the group of local isometries of the maximal dimen…

非可逆Finsler流形间等距映射的泛函刻画

A functional characterization of isometries between non-reversible Finsler manifolds

本文通过推广Myers-Nakai定理，利用光滑半Lipschitz函数锥及新的代数/拟度量结构，完整刻画了非可逆Finsler流形间的等距映射。

(α,β)度量及其等距变换的芬斯勒时空条件

The Finsler spacetime condition for (α,β)-metrics and their isometries

研究具有(α,β)度量的伪芬斯勒空间，建立其具有芬斯勒时空结构的条件，确定(α,β)度量等距变换与基础伪黎曼度量等距变换关系，为引力物理应用提供候选时空及相关等距变换结论。

Finslerian angle-preserving connection in two-dimensional case. Regular realization

We show that the metrical connection can be introduced in the two-dimensional Finsler space such that entailed parallel transports along curves joining points of the underlying manifold keep the two-vector angle as well as the length of the tangent vector, thereby realizing isometries of tangent spaces under the parallel transports. The curvature tensor is found. In case of the Finsleroid-regular space, constructions possess the $C^{\infty}$-regular status globally regarding the dependence on tangent vectors. Many involved and important relations are explicitly derived. Keywords: Finsler metri…

Splitting theorems for Finsler manifolds of nonnegative Ricci curvature

We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splitting theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can perform the isometric splitting in the sense that there is a one-parameter family of isometries generated from the gradient vector field of the Busemann function. A Betti number estimate is also given for Berwald spaces.