Umbilicity of surfaces with orthogonal asymptotic lines in \(\mathbb R^ 4\).

DOI10.1016/S0926-2245(02)00068-2zbMath1035.53012WikidataQ115338200 ScholiaQ115338200MaRDI QIDQ1608973

Federico Sánchez-Bringas, María Del Carmen Romero Fuster

Publication date: 14 August 2002

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

asymptotic directionsphericalumbilicityhypersphericity of surfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Topological properties of mappings on manifolds (58K15)

Related Items (15)

Lines of curvature on the double torus ⋮ Isometric immersions with prefixed second order geometry in minimal codimension ⋮ Conformal invariants and spherical contacts of surfaces in \(\mathbb R^4\) ⋮ Contact properties of codimension 2 submanifolds with flat normal bundle ⋮ Affine metric for locally strictly convex manifolds of codimension 2 ⋮ Transformations between surfaces in \(\mathbb{R}^4\) with flat normal and/or tangent bundles ⋮ The horospherical geometry of surfaces in hyperbolic 4-space ⋮ Construction of non-hyperspherical immersions ⋮ Characterization of spherical immersions of surfaces in \(\mathbb{R}^{4}\) ⋮ Codazzi fields on surfaces immersed in Euclidean 4-space ⋮ Orthogonal asymptotic lines on surfaces immersed in \(\mathbb{R}^4\) ⋮ The Taylor expansion of the exponential map and geometric applications ⋮ Principal configurations around umbilics of spacelike surfaces in null hypersurfaces of \(\mathbb{R}_1^4\) ⋮ Asymptotic lines on real Milnor links of a family that realizes any genus ⋮ Semiumbilics and 2-regular immersions of surfaces in Euclidean spaces

Cites Work

• Unnamed Item
• Osculating hyperplanes and asymptotic directions of codimension two submanifolds of Euclidean spaces
• Critical point theory and submanifold geometry
• Umbilical submanifolds with respect to a nonparallel normal direction
• Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\)
• The geometry of surfaces in 4-space from a contact viewpoint
• On singularities of submanifolds of higher dimensional Euclidean spaces
• The normal singularities of a submanifold
• Inflection points and topology of surfaces in 4-space
• Contributions to the Theory of Surfaces in a 4-Space of Constant Curvature
• Integral formulas for submanifolds and their applications

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