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 necessa...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.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 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.
