Search results for "Umbilicity"

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Umbilicity of surfaces with orthogonal asymptotic lines in R4

2002

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.

Normal fieldComputational Theory and MathematicsOrthogonalityUmbilicityAsymptotic directionMathematical analysisν-principal curvature foliationGeometry and TopologyAnalysisSphericitySphericityMathematicsDifferential Geometry and its Applications
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