Projectively flat arctangent Finsler metric  

作　　者：YU Yao-yong 

机构地区：[1]Department of Mathematics Zhejiang University, Hangzhou 310028, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2006年第12期2097-2103,共7页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project (No. 10571154) supported by the National Natural Science Foundation of China

摘　　要：In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α,β)-metric, where α is a Riemannian metric and β is a 1-form. We obtain a sufficient and necessary condition that F is locally projectively flat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively flat. Moreover, we prove that such projectively flat Finsler metrics with constant flag curvature must be locally Minkowskian.

关 键 词：Arctangent Finsler metric Projectively flat （α β）-metric Flag curvature 

分 类 号：O186[理学—数学]