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arXiv · 1707.09449

Isometric immersions into products of many space forms: an introductory study

Bruno Mendonça Rey dos Santos
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Abstract

This article begins the theory of submanifolds into products of 2 or more space forms. The tensors $\mathbf{R}$, $\mathbf{S}$ and $\mathbf{T}$ defined by Lira, Tojeiro and Vit\'orio at \cite{LTV} and the Bonnet theorem proved by them are generalized for the product of many space forms. Besides, some examples given by Mendon\c{c}a and Tojeiro at \cite{MT} and the reduction of codimension theorem proved by them are also generalized.

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Bruno Mendonça Rey dos Santos. 2017-07-29. Isometric immersions into products of many space forms: an introductory study. https://arxiv.org/abs/1707.09449

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