Inflection Points and Nonsingular Embeddings of Surfaces in ${\bf R}^5$
Dirce Kiyomi Hayashida Mochida, M. C. Romero-Fuster, María Aparecida Soares Ruas · Rocky Mountain Journal of Mathematics · 2003
We define asymptotic direction fields on surfaces embedded in R 5 and characterize their critical points both as umbilics of height 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.