We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen’s inequality for such submanifolds. The equality case is also studied. Moreover, inspired by Lawson and Simons’s integral currrent’s theorem on a submanifold, we find a similar pinching inequality for a sequential warped product submanifold and obtain geometric results when the equality case is satisfied.

中文翻译：

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具有全纯、全实和点向倾斜因子的顺序扭曲产品子流形

我们介绍了 Kaehler 流形的顺序扭曲积子流形，提供示例并建立此类子流形的 Chen 不等式。还研究了平等情况。此外，受劳森和西蒙斯关于子流形的积分电流定理的启发，我们发现了一个类似的收缩不等式，用于连续翘曲积子流形，并在满足等式情况时获得几何结果。