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...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.展开更多
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘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.