Mochida, D. K. H.
Romero-Fuster, M. C.
Ruas, Maria Aparecida Soares
Total Authors: 3
Rocky Mountain Journal of Mathematics;
Field of knowledge:
Physical Sciences and Mathematics
We define asymptotic direction fields on surfaces embedded in R5 and characterize their critical points both as umbilics of heigth functions and as singular points of order 2 of the embedding in Feldman's sense. We show that there are at least one and at most five of these fields defined locally at each point of a generically embedded closed surface. We use this viewpoint in order to consider the existence of singular points of order 2 on a given surface. (AU)