具有常Φ-截面曲率c的卷积子流形

Warped product submanifold with constant Φ - sectional curvature

在结构向量场ξ是具有常Φ-截面曲率c的β-Kenmotsu流形的卷积子流形的法向量场的情况下,定义了具有常Φ-截面曲率c的β-Kenmotsu空间形式的卷积子流形的平均曲率模长||H||2和卷积函数f的一个不等关系式,另外还推导了卷积子流形是全实子流形的相应不等式.

Under the condition that structure vector field ξ is a normal vector field of M1× f M2,this paper considers the warped product submanifold isometrically immersed in a real β-Kenmotsu space form with constant Φsectional curvature.It establishes a sharp relationship between the warping function f of M1× f M2 and the squared mean curvature ｜｜H｜｜2.It also gives similar equality of totally real submanifold.