Search results for "Principal curvature"

showing 2 items of 2 documents

Curvature locus and principal configurations of submanifolds of Euclidean space

2017

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.

Mean curvaturePrincipal curvatureGeneral MathematicsHyperbolic spaceMathematical analysisCurvature formCenter of curvatureMathematics::Differential GeometrySectional curvatureCurvatureMathematicsScalar curvatureRevista Matemática Iberoamericana
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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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