H3( -c2)中的CMC-c曲面

讨论了对称空间SL(n,C)/SU(n)中的曲面.首先,讨论了H3(-c2)中的CMC-c曲面(常中曲率为c的曲面)与R3中的极小曲面的关系,利用初等方法证明了H3(-c2)中的一个CMC-c曲面族,当c趋于零时,收敛到R3中的一个极小曲面的结论;其次,把经典的Ricci定理推广到对称空间SL(n,C)/Su(n)上.证明了单连通黎曼曲面(M2,ds2)可以共形等距地浸入到SL(n,C)/SU(n)上,且有全纯右Gauss映射的充分必要条件是ds2的截面曲率K<0及Ricci条件——-K·ds2的截面曲率为 1.

Surfaces of constant mean curvature one in hyperbolic 3-space H3(- c2)

In this paper,it deal with surfaces in symmetric space SL(n,C)/SU(n).They are concerned about the following two problems.First,discuss the relation between surfaces of constant mean curvature one in hyperbolic 3-space H3(-c2) and minimal surfaces in R3,and by using elementary methods,show that a minimal surface in R3 can be considered as a limit of a family of surfaces with constant mean curvature c in H3(-c2).Secondly,it generalize the canonical Ricci theorem to SL(n,C)/SU(n),and prove that a simply connected Riemann 2-manifold(M2,ds2) can be conformally immersed into SL(n,C)/SU(n) with the holomorphic right Gauss map if and only if the sectional curvature of ds2 is negative,and the sectional curvature of-K.ds2 is 1(this is the Ricci condition).