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

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 Vitório at \cite{LTV} and the Bonnet theorem proved by them are generalized for the product of many space forms. Besides, some examples given by Mendonça and Tojeiro at \cite{MT} and the reduction of codimension theorem proved by them are also generalized.

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