Redução de codimensão de imersões regulares

Abstract

Consider immersion (Expressão Matemática) dimensional manifold Mn in a manifold of constant secctional curvature c. Let N(x) be the first normal space of f in x 2 M, that is the subspace of the normal space that is generate to image of second form fundamental of f in x. We say that we can reduce the codimension of f to k, with (Expressão Matemática), if exists a submanifold L of Qc (n + k)-dimensional totally geodesic such that (Expressão Matemática), and f is 1-1-regular if the first normal space have constant dimension 1. The objective of this work is to give a detailed exhibition of results obtained by Lúcio Rodriguez and Renato Tribuzy in "Reduction of Codimension of Regular Immersions", published in Mathematische Zeitschrift in the year of 1984, that permit to reduce the codimension of 1-1-regular.