论文标题
Schwarzian衍生物和顺式转换在Finsler歧管上
The Schwarzian derivative and conformal transformation on Finsler manifolds
论文作者
论文摘要
瑟斯顿（Thurston）于1986年发现，施瓦茨（Schwarzian）衍生物具有与多种曲率相似的神秘特性。他的工作后，有几种方法可以在Riemannian歧管上提出这一概念。在这里，在Finsler歧管上的全球形成性差异性的研究中确定了一个张量场，是Schwarzian衍生物的自然概括。然后，给出了对Finsler歧管上的Mobius映射的自然定义，并研究了其特性。特别是表明，莫比乌斯映射是保留圆圈的映射，反之亦然。因此，如果向前的大地芬斯勒歧管接收一个莫比乌斯映射，则指示与欧几里得球体$ s^{n-1} $在$ \ mathbb {r}^n $中相同。另外，如果向前的地球曲率曲率的完全均匀的鳍片歧管承认Mobius映射的非平凡变化，那么它是恒定截面曲率的Riemannian歧管。
Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere $ S^{n-1}$ in $ \mathbb{R}^n $. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.
