Projectively flat Asanov Finsler metric  

作　　者：HAN Jing-wei YU Yao-yong 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]School of Science, Hangzhou Dianzi University, Hangzhou 310028, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第6期963-968,共6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 the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.In this work, we study the Asanov Finsler metric F=α(β2/α2+gβ/α+1)1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.

关 键 词：Exponential Finsler metric Projectively flat （α β）-metrics Douglas tensor 

分 类 号：O186.1[理学—数学]