Projectively flat Asanov Finsler metric

【摘要】 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.更多还原

【Abstract】 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.更多还原