A CLASS OF LIFT METRICS ON FINSLER MANIFOLDS

Document Type: Regular Paper

Authors

1 Department of Mathematics and Computer Science, Arak University, Arak, I. R. of Iran

2 Department of Mathematics, Faculty of Science, Qom University, Qom, I. R. of Iran

Abstract

In this paper, we are going to study the g-natural metrics on the tangent bundle of Finsler
manifolds. We concentrate on the complex and Kählerian and Hermitian structures associated with Finsler
manifolds via g-natural metrics. We prove that the almost complex structure induced by this metric is a
complex structure on tangent bundle if and only if the Finsler metric is of scalar flag curvature. Then we show
that the complex structure is Hermitian if and only if the Finsler metric is of constant flag curvature.

Keywords