一类与Funk度量射影相关的Finsler度量具有两种常曲率的条件

Funk度量F是一个射影平坦的Finsler度量,它具有常曲率K=-14和常S 曲率S=12(n+1)F.首先在欧氏空间Rn的一个强凸区域Ω上用Funk度量F和闭1 形式β构造了一类新的Finsler度量 F=F+β,然后分别找到了 F具有常曲率和常S 曲率的充分必要条件.

Isoparametric hypersurfaces in Funk spaces

Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures. Moreover, a complete classification of isoparametric families in a Funk space is given.

关于一类特殊的射流

讨论一类特殊的射流(spray)Gδ:=yixi-2δ(x)Fyiyi可由正定Finsler度量诱导的充分必要条件及此度量的特殊性质.若δ(x)为常数,则当且仅当δ=0,12,1时,Gδ可由正定Finsler度量F诱导,并对这些度量F做了不同程度的刻画.

The Characterizations and Constructions of Sprays of Isotropic Curvature

This paper discusses the sprays of isotropic curvature.We first determine the relationship betweenχ-curvatures of two projectively related sprays.Based on this,we find an approach to construct sprays of isotropic curvature and find infinitely many sprays of isotropic curvature via some known sprays of isotropic curvature.In particular,by using famous Funk metricΘ,we can construct infinitely many sprays of isotropic curvature,some of which can be induced by Finsler metrics,but others cannot be induced by any Finsler metric.

一类具有弱射影Ricci曲率的Spray及其可度量化问题

【目的】Spray的曲率性质及其可度量化问题在Spray几何中是很重要的,因此对一类由Funk度量Θ构造的射影平坦的Spray G(其测地系数为G^i=τΘy^i,其中τ是常数)进行研究。【方法】计算G的射影Ricci曲率,进而在一定射影Ricci曲率条件下研究这类Spray的可度量化问题。【结果】1)在G是射影Ricci-平坦的条件下,确定了流形的体积形式;2)在G可由芬斯勒度量F诱导的前提下,若F具有弱射影Ricci曲率且是非射影Ricci-平坦的,则F~的结构可被确定。【结论】初步分类了具有弱射影Ricci曲率的芬斯勒度量F。