Rigidity of submanifolds in the Euclidean and spherical spaces

DOI10.1007/s12215-018-00395-9zbMath1437.53045OpenAlexW2913757788MaRDI QIDQ2174822

Fábio R. dos Santos, Jonatan Floriano da Silva, Henrique Fernandes de Lima, Marco Antonio L. Velásquez

Publication date: 27 April 2020

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-018-00395-9

zbMATH Keywords

parallel mean curvature vector fieldcomplete submanifoldsEuclidean and spherical spacespseudo-umbilical submanifolds

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24)

Cites Work

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• Submanifolds with constant scalar curvature in a unit sphere
• The geometry of closed conformal vector fields on Riemannian spaces
• On the geometry of complete submanifolds immersed in the hyperbolic space
• Stability of hypersurfaces with constant mean curvature
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Submanifolds with parallel mean curvature vector in spheres
• Rigidity of compact submanifolds in a unit sphere
• Integral formulas for compact spacelike \(n\)-submanifolds in de Sitter spaces. Applications to the parallel mean curvature vector case
• A special Stoke's theorem for complete Riemannian manifolds
• Submanifolds with Constant Mean Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• Complete submanifolds in Euclidean spaces with parallel mean curvature vector

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