Kaehler流形的Sasaki子流形

Sasakian Submanifolds of Kaehlerian Manifolds

Kaehler流形是偶维微分流形,奇维微分流形中,与之媲美的是Sasaki流形。它是正规、切触度量流形。关于Sasaki流形,有判别定理(见[1]中P272定理5.1) 定理A 殆切触度量流形M是Sasaki流形的充要条件为 （xφ）Y=g（X,Y）ξ-g（Y,ξ）X。 （1） 我们知道,Kaehler流形的Sasaki实超曲面是Sasaki流形,其维数也是奇数。Bejancu成功地对Kaehler流形的反全纯子流形引入Sasaki结构,定义了Sasaki反全纯子流形。

A.Bejancu introduced the concept of Sasakian anti-holomorphic submanifolds of Kaehlerian manifolds.He got some theorems on Sasakian anti-holomorphic submanifolds of Kaehlerian manifolds with flat normal connection. In this paper, the authors prove that condition 'flat normal connection'is not necessary in the theorems of Bejancu. Some similar theorems on Sasakian CR submanifolds of Kaehlerian manifolds introduced this paper are obtained.