Codazzi fields on surfaces immersed in Euclidean 4-space
Gutiérrez J.M. Núñez, Romero M.C. Fuster, Federico Sánchez-Bringas · Institutional Repositories DataBase (IRDB) · 2008
Consider a Riemannian vector bundle of rank 1 defined by a normal vector field on a surface M in R 4 .Let II be the second fundamental form with respect to which determines a configuration of lines of curvature.In this article, we obtain conditions on to isometrically immerse the surface M with II as a second fundamental form into R 3 .Geometric restrictions on M are determined by these conditions.As a consequence, we analyze the extension of Loewner's conjecture, on the index of umbilic points of surfaces in R 3 , to special configurations on surfaces in R 4 .