Isometric immersions of a complete and connected Riemannian manifold
首发时间:2023-02-02
Abstract:In this paper, some basic concepts and theorems of Riemannian manifolds are introduced briefly, and then the concept of isometric immersion is introduced in oeder to introduce the basic cconcept of submanifolds. After introducing Hideki Omori's maximum principle on Riemannian manifolds, a basic theorem of isometric immersion of Riemannian manifolds is proved by using this theorem with modern mathematical language. By replacing $R^n$in the theorem with a more general space and adding additional conditions, the generalized theorem is obtained, and the proof is given in a similar way.
keywords: Basic mathematics Isometric immersion Maximun principle Second fundamental form Sectional curvature
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