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

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.