A basic inequality and new characterization of Whitney spheres in a complex space form

DOI10.1007/BF02773534zbMath1076.53072OpenAlexW2142255475WikidataQ125989816 ScholiaQ125989816MaRDI QIDQ1781939

Luc Vrancken, Haizhong Li

Publication date: 9 June 2005

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02773534

zbMATH Keywords

Lagrangian submanifoldWhitney sphereMean curvature

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (14)

On product affine hyperspheres in \(\mathbb{R}^{n+1}\) ⋮ Minimal Legendrian submanifolds of $\mathbb S^{9}$ with nonnegative sectional curvature ⋮ Characterization of Whitney spheres among Lagrangian submanifolds with conformal Maslov form ⋮ An optimal inequality related to characterizations of the contact Whitney spheres in Sasakian space forms ⋮ Gap theorems for Lagrangian submanifolds in complex space forms ⋮ On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\) ⋮ Complete Lagrangian self-expanders in \(\mathbb{C}^2\) ⋮ Some optimal inequalities for anti-invariant submanifolds of the unit sphere ⋮ An optimal inequality on locally strongly convex centroaffine hypersurfaces ⋮ Classification of Calabi hypersurfaces with parallel Fubini-Pick form ⋮ New characterizations of the Clifford torus as a Lagrangian self-shrinker ⋮ On J-parallel totally real three-dimensional submanifolds of \(S^{6}\)(1) ⋮ Unnamed Item ⋮ New characterizations of the Whitney spheres and the contact Whitney spheres

Cites Work

• Flow by mean curvature of convex surfaces into spheres
• Totally real submanifolds and symmetric bounded domains
• Calibrated geometries
• Isotropic totally real submanifolds
• Lagrangian submanifolds of \(C^n\) with conformal Maslov form and the Whitney sphere
• Totally real parallel submanifolds in \(P^ n(\)c)
• Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form
• Complex extensors and Lagrangian submanifolds in complex Euclidean spaces
• Interaction of Legendre curves and Lagrangian submanifolds
• Willmore surfaces in \(S^n\)
• Willmore submanifolds in a sphere.
• Closed conformal vector fields and Lagrangian submanifolds in complex space forms.
• Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes
• Parallel submanifolds of complex space forms I
• On Totally Real Submanifolds
• Lagrangian submanifolds satisfying a basic equality
• Jacobi's elliptic functions and Lagrangian immersions

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