Curvature pinching and eigenvalue rigidity for minimal submanifolds

DOI10.1007/BF01162343zbMath0563.53046OpenAlexW2035406101MaRDI QIDQ1057524

Francisco Urbano, Antonio Ros, Sebastían Montiel

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173697

zbMATH Keywords

symmetric spacesRicci curvaturecomplex projective spaceminimal submanifoldstotally real submanifoldsspectral invariantsglobal rigiditypinching problemSimons formula

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Related Items (9)

An optimal pinching theorem of minimal Legendrian submanifolds in the unit sphere ⋮ Bochner's technique for statistical structures ⋮ Curvature pinching for complete Kähler submanifolds of a complex projective space ⋮ On the minimal submanifolds in \(\mathbb{C} P^ m(c)\) and \(S^ N(1)\) ⋮ Minimal submanifolds with bounded second fundamental form ⋮ On Complete Minimal Submanifolds in a Sphere ⋮ Some estimates of total tension and their applications ⋮ Some inequalities and applications of Simons' type formulas in Riemannian, affine, and statistical geometry ⋮ Index of Lagrangian submanifolds of \(\mathbb{C} \mathbb{P}^ n\) and the Laplacian of 1-forms

Cites Work

• Eigenvalue inequalities for minimal submanifols and P-manifolds
• Totally real submanifolds and symmetric bounded domains
• Nonnegatively curved totally real submanifolds
• A characterization of seven compact Kähler submanifolds by holomorphic pinching
• Totally real parallel submanifolds in \(P^ n(\)c)
• Planar geodesic immersions
• Addendum to my paper On veronese manifolds
• Differential geometry of Kaehler submanifolds
• Minimal varieties in Riemannian manifolds
• Totally Real Minimal Submanifolds of a Complex Projective Space
• Submanifolds with Constant Mean Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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