A new characterization of Willmore submanifolds

DOI10.1007/S11766-011-2531-YzbMath1265.53062OpenAlexW2104457993MaRDI QIDQ453365

Hong-Wei Xu, Dengyun Yang

Publication date: 5 October 2012

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-011-2531-y

zbMATH Keywords

eigenvalueSchrödinger operatorflat normal bundleWillmore submanifoldsWillmore torus

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Schrödinger operator, Schrödinger equation (35J10) Global submanifolds (53C40)

Related Items (1)

Sharp estimates for the first eigenvalue of Schrödinger operator in the unit sphere

Cites Work

• The gap phenomenon for extremal submanifolds in a sphere
• New characterizations of the Clifford tori and the Veronese surface
• Minimal immersions of surfaces by the first eigenfunctions and conformal area
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Willmore surfaces in \(S^n\)
• Willmore surfaces in the unit \(n\)-sphere
• Willmore submanifolds in a sphere.
• \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
• Curvature and rigidity of Willmore submanifolds
• Minimal varieties in Riemannian manifolds

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