Circle-preserving transformations in Finsler spaces

被引：9

作者：

Bidabad, Behroz ^{[1
]}

Shen, Zhongmin ^{[2
]}

机构：

[1] Amirkabir Univ Technol, Dept Math & Comp Sci, Tehran Polytech, Tehran 15914, Iran

[2] Purdue Univ Indianapolis IUPUI, Indiana Univ, Dept Math Sci, Indianapolis, IN 46202 USA

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2012年 / 81卷 / 3-4期

关键词：

Finsler space; conformal transformations; circle-preserving; concircular; MANIFOLDS; GEOMETRY;

D O I：

10.5486/PMD.2012.5317

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.

引用

页码：435 / 445

页数：11

共 15 条

[1]

AGRAWAL P, 1972, TENSOR, V23, P333

[2]

[Anonymous], 2006, Initiation to Global Finslerian Geometry

[3] Classification of complete Finsler manifolds through a second order differential equation [J].