Lines of principal curvature for mappings with Whitney umbrella singularities

DOI10.2748/tmj/1178228407zbMath0611.53007OpenAlexW2128644218MaRDI QIDQ1087149

B. George

Publication date: 1986

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178228407

zbMATH Keywords

structurally stableprincipal cyclecurvature linesDarboux umbilicprincipally stableWhitney umbrella singularity

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Stability theory for smooth dynamical systems (37C75)

Related Items (10)

Hyperbolic principal cycles on hypersurfaces of \(\mathbb{R}^ 4\) ⋮ Positive quadratic differential forms: Topological equivalence through Newton polyhedra ⋮ Symmetries of cross caps ⋮ On the index of principal foliations of surfaces in R^3 with corank 1 singularities ⋮ Lines of curvature near principal cycles ⋮ Closed lines of curvature for Weingarten immersions ⋮ Isolated roundings and flattenings of submanifolds in Euclidean spaces ⋮ Intrinsic invariants of cross caps ⋮ Closed lines of curvature for Weingarten immersions ⋮ Lines of principal curvature around umbilics and Whitney umbrellas

Cites Work

• The general type of singularity of a set of \(2n-1\) smooth functions of \(n\) variables
• Principal Lines on Surfaces Immersed With Constant Mean Curvature
• Stable surfaces in Euclidean three space.
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