摘要
A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K = 3c ＋ δ where δ and c are scalar functions on M. In this paper, we establish the intrinsic relation between scalar functions c（x） and a（x）. More general, by invoking the Ricci identities for a one form, we investigate Finsler metric of weakly isotropic flag curvature K = 3θ/F ＋ δ and show that F has constant flag curvature if θ is horizontally parallel.
A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K = 3c ＋ δ where δ and c are scalar functions on M. In this paper, we establish the intrinsic relation between scalar functions c（x） and a（x）. More general, by invoking the Ricci identities for a one form, we investigate Finsler metric of weakly isotropic flag curvature K = 3θ/F ＋ δ and show that F has constant flag curvature if θ is horizontally parallel.
基金
Supported by the National Natural Science Foundation of China(11071005)
Research Fund for the Doctoral Program of Higher Education of China 20110001110069
