6533b823fe1ef96bd127f635

RESEARCH PRODUCT

Umbilicity of surfaces with orthogonal asymptotic lines in R4

M.c. Romero-fusterFederico Sánchez-bringas

subject

Normal fieldComputational Theory and MathematicsOrthogonalityUmbilicityAsymptotic directionMathematical analysisν-principal curvature foliationGeometry and TopologyAnalysisSphericitySphericityMathematics

description

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.

yearjournalcountryeditionlanguage
2002-05-01Differential Geometry and its Applications
https://doi.org/10.1016/s0926-2245(02)00068-2