A metric property of umbilic points

DOI10.1590/S0001-37652003000400001zbMath1049.53006arXivmath/0305185MaRDI QIDQ4454505

Jorge Sotomayor, Ronaldo A. Garcia

Publication date: 8 March 2004

Published in: Anais da Academia Brasileira de Ciências (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305185

zbMATH Keywords

umbilic pointprincipal curvature lines

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Normal forms on manifolds (58K50) Surfaces in Euclidean and related spaces (53A05) Stability theory for smooth dynamical systems (37C75)

Cites Work

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• Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in \(\mathbb{R}^3\)
• Geometric mean curvature lines on surfaces immersed in \(\mathbb{R}^3\)
• Lines of axial curvature on surfaces immersed in \(\mathbb{R}^4\)
• Principal curvature lines near Darbouxian partially umbilic points of hypersurfaces immersed in \(\mathbb R^4\)
• A Sharp Geometric Estimate for the Index of an Umbilic on a Smooth Surface
• Lines of curvature on surfaces immersed in ?4
• On binary differential equations and umbilics
• Umbilic points on Gaussian random surfaces

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