不定复空间形式中全实类空子流形的一些几何不等式

发布时间：2018-03-03 13:07

本文选题：不定复空间形式　切入点：全实类空子流形　出处：《安徽师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：在子流形理论中,下述问题是基本的:在子流形中建立内蕴不变量与外在不变量之间的各种关系.这种关系主要体现为不等式.本文的主要目的是对不定复空间形式的全实类空子流形建立内蕴不变量和外在不变量之间的几何不等式.具体而言,我们分别利用代数不等式和T. Oprea最优化方法建立了不定复空间形式中全实类空子流形两种情形下关于δ-Casorati曲率的不等式,并得到等号成立时的几何条件;对不定复空间形式的全实类空子流形分别建立了两种情形下关于Ricci曲率和平均曲率之间的不等式,给出了 Ricci曲率的一个上界;另一方面,运用代数技巧得到了关于Ricci曲率和平均曲率,数量曲率之间的关系,给出了 Ricci曲率的一个下界,由此得到了关于k-Ricci曲率和T.Oprea不变量的两个不等式.最后,针对不定复空间形式的全实类空子流形,我们通过研究平行脐性法向量场在法丛中的位置,得到一种特殊情况下的一些相关结果.
[Abstract]:In submanifold theory, The following problems are fundamental: to establish various relations between intrinsic invariants and external invariants in submanifolds. This relationship is mainly embodied in inequalities. Manifolds establish geometric inequalities between intrinsic invariants and external invariants. By using algebraic inequalities and T.#en0# optimization methods, we establish inequalities on 未 -Casorati curvature in the form of totally real space-like submanifolds in the form of indefinite complex spaces, respectively, and obtain the geometric conditions when the equal sign holds. In this paper, the inequality of Ricci curvature and mean curvature for all real space-like submanifolds in the form of indefinite complex space is established, and an upper bound of Ricci curvature is given. The relation between Ricci curvature, mean curvature and scalar curvature is obtained by using algebraic technique. A lower bound of Ricci curvature is given, and two inequalities about k-Ricci curvature and T. Oprea invariant are obtained. For all real space-like submanifolds in the form of indeterminate complex spaces, we obtain some relevant results in a special case by studying the position of parallel umbilical normal vector fields in normal clusters.
【学位授予单位】：安徽师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O186.12

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