0000000000536104
AUTHOR
Federico Sánchez-bringas
Umbilicity of surfaces with orthogonal asymptotic lines in R4
We study some properties of surfaces in 4-space all whose points are umbilic with respect to some normal field. In particular, we show that this condition is equivalent to the orthogonality of the (globally defined) fields of asymptotic directions. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in 4-space. 2002 Elsevier Science B.V. All rights reserved.
Curvature locus and principal configurations of submanifolds of Euclidean space
We study relations between the properties of the curvature loci of a submanifold M in Euclidean space and the behaviour of the principal configurations of M, in particular the existence of umbilic and quasiumbilic fields. We pay special attention to the case of submanifolds with vanishing normal curvature. We also characterize local convexity in terms of the curvature locus position in the normal space.