Real solvability of the equation \(\partial^2_{\overline z}\omega=\rho g\) and the topology of isolated umbilics

DOI10.1007/BF02921718zbMath0983.53004MaRDI QIDQ1568964

Brian Smyth, Frederico Xavier

Publication date: 22 June 2000

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

indexCarathéodory conjectureLoewner conjecturedipole line fieldisolated umbilicprincipal line fieldssystem of two wave equations

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Surfaces in Euclidean and related spaces (53A05)

Related Items (8)

Umbilical points on three dimensional strictly pseudoconvex CR manifolds. I: Manifolds with \(\mathrm{U}(1)\)-action ⋮ On conformal points of area preserving maps and related topics ⋮ Index formulas for higher order Loewner vector fields ⋮ A criterion for the nonexistence of closed leaves in unorientable planar foliations ⋮ Hartman-Wintner's theorem and its applications ⋮ Umbilic singularities and lines of curvature on ellipsoids of \(\mathbb{R}^{4}\) ⋮ Normal curvatures of asymptotically constant graphs and Carathéodory’s conjecture ⋮ The behavior of the principal distributions on the graph of a homogeneous polynomial

Cites Work

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• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• A proof of a conjecture of Loewner and of the conjecture of Caratheodory on umbilic points
• Beweis einer Caratheodoryschen Vermutung. I
• Über Nabelpunkte auf einer Eifläche
• On G. Bol's proof of Carathéodory's conjecture
• Seminar on Differential Geometry. (AM-102)
• A Sharp Geometric Estimate for the Index of an Umbilic on a Smooth Surface

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