N-Dimensional submanifolds with an (n−1)-dimensional asymptotic distribution and with 1-asymptotic lines in a space form Rm(k)

Abstract

In this paper we prove a theorem about the reduction of the codimension of n-dimensional submanifolds of a space form Rm(k), with an (n-1)-dimensional asymptotic distribution and with 1-asymptotic lines (i.e. asymptotic curves for which the (1+1)-dimensional osculating spaces are subspaces of the tangent spaces). We also give a result for (n−1)-asymptotic lines in connection with Enneper's formula. Finally we construct an example.