Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this...Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d1,d2,...,dn+1 and r.展开更多
Dually flat Finsler metrics arise from information geometry which has attracted some geometers and statisticians. In this paper, we study dually flat general spherically symmetric Finsler metrics which are defined by ...Dually flat Finsler metrics arise from information geometry which has attracted some geometers and statisticians. In this paper, we study dually flat general spherically symmetric Finsler metrics which are defined by a Euclidean metric and two related 1-forms. We give the equivalent conditions for those metrics to be locally dually flat. By solving the equivalent equations, a group of new locally dually flat Finsler metrics is constructed.展开更多
文摘Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d1,d2,...,dn+1 and r.
基金supported by National Natural Science Foundation of China (Grant No. 11371209)K. C. Wong Magna Fund in Ningbo University
文摘Dually flat Finsler metrics arise from information geometry which has attracted some geometers and statisticians. In this paper, we study dually flat general spherically symmetric Finsler metrics which are defined by a Euclidean metric and two related 1-forms. We give the equivalent conditions for those metrics to be locally dually flat. By solving the equivalent equations, a group of new locally dually flat Finsler metrics is constructed.
