拟常曲率黎曼流形中卷积子流形的一些不等式

Inequalities of warped product submanifolds in a Riemannian manifold of quasi-constant curvature

用最优化方法,研究了拟常曲率黎曼流形中的卷积子流形,讨论了广义标准δ-Casorati曲率,建立了内在不变量和外在不变量之间的两个不等式,推广了实空间形式中子流形的最优不等式。

By optimization methods on Riemannian submanifolds,we establish two inequalities between the intrinsic and extrinsic invariants,for generalized normalizedδ-Casorati curvatures of warped product submanifolds in a Riemannian manifold of quasi-constant curvature.We generalize the conclusions of the optimal inequalities of submanifolds in real space forms.