Gap theorems for Lagrangian submanifolds in complex space forms

DOI10.1007/S10711-021-00652-9zbMath1481.53077OpenAlexW3201208888MaRDI QIDQ2665235

Shunjuan Cao, En-Tao Zhao

Publication date: 18 November 2021

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-021-00652-9

zbMATH Keywords

Lagrangian submanifoldWhitney spherecurvature pinchinggap theorem

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24) Lagrangian submanifolds; Maslov index (53D12)

Related Items (1)

On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Lagrangian submanifolds of \(C^n\) with conformal Maslov form and the Whitney sphere
• On the minimal submanifolds in \(\mathbb{C} P^ m(c)\) and \(S^ N(1)\)
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• A rigidity theorem for submanifolds with parallel mean curvature in a sphere
• Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form
• Riemannian geometry of Lagrangian submanifolds
• A basic inequality and new characterization of Whitney spheres in a complex space form
• Closed conformal vector fields and Lagrangian submanifolds in complex space forms.
• A general gap theorem for submanifolds with parallel mean curvature in \(\mathbb R^{n+p}\)
• Minimal varieties in Riemannian manifolds
• An energy gap phenomenon for the Whitney sphere
• A general rigidity theorem for complete submanifolds
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

This page was built for publication: Gap theorems for Lagrangian submanifolds in complex space forms