不定复空间型中的全实极大类空子流形

Totally Real Maximal Space-Like Submanifolds in Indefinite Complex Space Form

设Ｎ￣ｎ（ｃ）是复ｎ维带有指标为ｎ的常全纯截面曲率为ｃ的复空间型，Ｍ是等距浸入在Ｎ￣ｎ（ｃ）中实ｎ维完备的全实类空子流形．本文获得：当Ｍ极大时，Ｍ是全测地的（ｎ≥２，ｃ≥０）或者０≤Ｓ≤－ｎ（ｎ－１）ｃ／４（ｎ≥２，ｃ＜０），其中Ｓ表示Ｍ的第二基本形式长度的平方．

Let Nn (c) be a complex n-dimensional indefinite complex space form of constant holomorphic sectional curvature c and of index n .and M be an n-dimensional complete totally real space-like submanifold isometrically immersed in Nn (c). When M is maximal,it is proved that either M is totally geodesic (n≥2,c ≥0) or 0≤S≤-n (n- 1 )c/4 (n≥2,c<0), where S denotes the square of the length of the second fundmental form of M.