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.
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.
In this paper, the Khler conditions of the Chern-Finsler connection in complex Finsler geometry are studied, and it is proved that Khler Finsler metrics are actually strongly Khler.
In this paper, we study a class of Finsler metrics in the form F = α + ∈β + 2k β2/α-k2β4/3α3 , where α= (√aijyiyj) is a Riemannian metric, β = biyi is a 1-form, and ∈ and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.
