【摘要】 设 (Mm,g)为任意m维黎曼流形 ,N =M×R+为具有黎曼度量ds2 =t2 gijdxidxj+c2 dt2 的黎曼流形 .本文将要证明 :当m =2时N为拟常曲率空间 ;当m ≥ 3时N为拟常曲率空间当且仅当Mm 为常曲率空间 .根据此特征 ,可构造若干非常曲率的拟常曲率空间 .例如 ,球面上任何二维曲面生成的锥都是拟常曲率空间更多还原

【Abstract】 Let (M m,g) be an m _dimensional Riemannian manifold and N=M×R + a Riemannian manifold with metric d s 2=t 2g ij d x i d x j+c 2 d t 2 . In this paper, it shall be show that when m=2 , N is of quasi_constant curvature; and when m≥3 , N is of quasi_constant curvature if and only if M m is of constant curvature. With this result a number of examples of spaces quasi_constant curvature can be constructed. For example, cones generated by any 2_dimensional surface on a sphere are all of quasi_constant curvature.更多还原