Abstract In the first part of this paper, using an optimization method on Riemannian submanifolds, we prove that for any Legendrian submanifold of a Sasakian space form M 2 n + 1 ( c ) of constant ϕ -sectional curvature c , we have two sharp inequalities relating some basic extrinsic and intrinsic invariants of the immersion, namely the ϕ -sectional curvature, the normalized scalar curvature, the mean curvature and the δ -Casorati curvatures. In the second part, we classify the family of Casorati ideal Legendrian submanifolds in a Sasakian space form and provide examples supporting the main results of the paper.

中文翻译：

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Sasakian空间形式中Casorati理想Legendrian子流形的分类

摘要 在本文的第一部分中，使用黎曼子流形的优化方法，我们证明了对于 Sasakian 空间形式 M 2 n + 1 ( c ) 的常数 ϕ 截面曲率 c 的任何勒让德式子流形，我们有两个尖锐的不等式涉及浸入的一些基本外在和内在不变量，即 ϕ -截面曲率、归一化标量曲率、平均曲率和 δ -Casorati 曲率。在第二部分，我们以 Sasakian 空间形式对 Casorati 理想 Legendrian 子流形族进行分类，并提供支持本文主要结果的示例。