Naturally reductive homogeneous $( lpha , eta )$-metric spaces

摘要

In the present paper we study naturally reductive homogeneous $( lpha , eta )$-metric spaces. We show that for homogeneous $( lpha , eta )$-metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $( lpha , eta )$-metric spaces.