摘要
本文讨论了曲面的切球丛的黎曼几何性质。证明了如下定理1 设(V,g)是2-维黎曼流形,(T(?)V,(?))是 V 上的切球丛,(?)为 Sasaki 度量,那么1)如果(T(?)V,(?))有正的截面曲率则 V 的 Gauss 曲率 k 必满足:0<k<4/(3c^2).2)(T(?)V,(?))为共形平坦空间的充要条件是曲面 V 有常 Gauss 曲率。
In this note,we prove the followingTheorem 1 Let (T^cV,(?)) be the tangent sphere bundle of a surface V,where (?) is the Sasaki metric,Then1)If(T^cV,(?)has positive sectional curvature,then the Gaussian cur-vature k of the surface V satisfies the inequality 0<k<4/(3c^2).2)The necessary and sufficient condition for (T^cV,(?))to be conformallyflat is that V has constant Gaussian curvature.
出处
《数学杂志》
CSCD
北大核心
1991年第1期49-52,共4页
Journal of Mathematics
