The fundamental theorem for hypersurfaces in Heisenberg groups

DOI10.1007/s00526-015-0818-1zbMath1320.32039OpenAlexW2105626414MaRDI QIDQ493228

Hung-Lin Chiu, Sin-Hua Lai

Publication date: 11 September 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-015-0818-1

zbMATH Keywords

equivalence problemhypersurfaces of the Heisenberg group

Mathematics Subject Classification ID

Other complex differential geometry (53C56) CR structures, CR operators, and generalizations (32V05) Analysis on CR manifolds (32V20)

Related Items (13)

Umbilic hypersurfaces of constant sigma-\(k\) curvature in the Heisenberg group ⋮ The fundamental theorem of Legendrian submanifolds in the Heisenberg group ⋮ A characterization of constant \(p\)-mean curvature surfaces in the Heisenberg group \(H_1\) ⋮ Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group ⋮ Positive mass theorem and the CR Yamabe equation on 5-dimensional contact spin manifolds ⋮ Free boundary constant p-mean curvature surfaces intersecting the Pansu sphere ⋮ An application of the moving frame method to integral geometry in the Heisenberg group ⋮ The differential geometry of curves in the Heisenberg groups ⋮ The differential geometry of curves in \(B^1 \times \mathbb{R}\) ⋮ Generalizations of the theorems of Pappus-Guldin in the Heisenberg groups ⋮ Umbilicity and characterization of Pansu spheres in the Heisenberg group ⋮ A metric interpretation of the geodesic curvature in the Heisenberg group ⋮ Global differential geometry of curves in three-dimensional Heisenberg group and CR sphere

Cites Work

• Critical point theory and submanifold geometry
• On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
• Pseudo-hermitian structures on a real hypersurface
• A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}}^{n}\)
• A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
• The Fefferman Metric and Pseudohermitian Invariants
• Psuedo-Einstein Structures on CR Manifolds
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