In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have t...In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have the same Douglas curvature. They are the conditions such that （α,β）-metrics have reversible geodesics.展开更多
In this paper,we study a class of Finsler metrics of cohomogeneity two on R×R~n.They are called weakly orthogonally invariant Finsler metrics.These metrics not only contain spherically symmetric Finsler metrics a...In this paper,we study a class of Finsler metrics of cohomogeneity two on R×R~n.They are called weakly orthogonally invariant Finsler metrics.These metrics not only contain spherically symmetric Finsler metrics and Marcal-Shen's warped product metrics but also partly contain another"warping"introduced by Chen-Shen-Zhao.We obtain differential equations that characterize weakly orthogonally invariant Finsler metrics with vanishing Douglas curvature,and therefore we provide a unifying frame work for Douglas equations due to Liu-Mo,Mo-Solórzano-Tenenblat and Solórzano.As an application,we obtain a lot of new examples of weakly orthogonally invariant Douglas metrics.展开更多
Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called ge...Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general （α, β）-metrics, which are defined by a Riemannian metric and a . We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471246)the Jiangxi Provincial Science and Technology Project(Grant No.20161BAB211021)
文摘In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have the same Douglas curvature. They are the conditions such that （α,β）-metrics have reversible geodesics.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12101022,12071228,12171005,11771020)the Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM202010005026)。
文摘In this paper,we study a class of Finsler metrics of cohomogeneity two on R×R~n.They are called weakly orthogonally invariant Finsler metrics.These metrics not only contain spherically symmetric Finsler metrics and Marcal-Shen's warped product metrics but also partly contain another"warping"introduced by Chen-Shen-Zhao.We obtain differential equations that characterize weakly orthogonally invariant Finsler metrics with vanishing Douglas curvature,and therefore we provide a unifying frame work for Douglas equations due to Liu-Mo,Mo-Solórzano-Tenenblat and Solórzano.As an application,we obtain a lot of new examples of weakly orthogonally invariant Douglas metrics.
基金supported by NSFC(Grant No.11371209)ZPNSFC(Grant No.LY13A010013)K.C.Wong Magna Fund in Ningbo University
文摘Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general （α, β）-metrics, which are defined by a Riemannian metric and a . We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed.
