Riemannian maps are generalizations of well-known notions of isometric immersions and Riemannian submersions. Most optimal inequalities on submanifolds in various ambient spaces are driven from isometric immersions. The main aim of this paper is to obtain optimal inequalities for Riemannian maps to space forms, as well as for Riemannian submersions from space forms, involving Casorati curvatures.

中文翻译：

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涉及Casorati曲率的Riemannian映射和Riemannian淹没的最佳不等式

黎曼贴图是对等距浸入和黎曼浸没的著名概念的概括。等距浸没驱动各种环境空间中子流形上的最佳最佳不等式。本文的主要目的是获得关于空间形式的黎曼映射的最佳不等式，以及从涉及卡索拉蒂曲率的空间形式的黎曼淹没中获得最佳不等式。