Integral inequalities for compact hypersurfaces with constant scalar curvature in the Euclidean sphere

DOI10.1007/S00009-020-1482-ZzbMath1452.53051OpenAlexW3008809505WikidataQ114232277 ScholiaQ114232277MaRDI QIDQ2178613

Josué Meléndez, Luis J. Alías

Publication date: 11 May 2020

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

Full work available at URL: https://doi.org/10.1007/s00009-020-1482-z

zbMATH Keywords

scalar curvatureisoparametric hypersurfaceselliptic operatorfirst Newton transformationCheng's and Yau's square operatorOkumura lemmatotal umbilicity tensor

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (10)

A sharp integral inequality for compact Weingarten hypersurfaces under an Okumura type inequality ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ Characterization results and a sharp integral inequality for LW spacelike hypersurfaces in locally symmetric Lorentzian spaces ⋮ Nonexistence and umbilicity of spacelike submanifolds with second fundamental form locally timelike ⋮ Unnamed Item ⋮ A sharp integral inequality for closed spacelike submanifolds immersed in the de Sitter space ⋮ A Simons type integral inequality for closed submanifolds in the product space \(\mathbb{S}^n\times\mathbb{R}\) ⋮ Characterizing closed linear Weingarten spacelike submanifolds immersed in the de Sitter space ⋮ Revisiting linear Weingarten hypersurfaces immersed into a locally symmetric Riemannian manifold ⋮ Sharp Simons type integral inequalities for closed linear Weingarten submanifolds in a space form

Cites Work

• Rigidity theorems for hypersurfaces with constant mean curvature
• Complete hypersurfaces with constant scalar curvature in spheres
• A maximum principle for hypersurfaces with constant scalar curvature and applications
• Hypersurfaces with constant scalar curvature
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• On the decay of matrix coefficients for exceptional groups
• J. Simons' type integral formula for hypersurfaces in a unit sphere
• Geometry of Hypersurfaces
• Maximum Principles and Geometric Applications
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Hypersurfaces with Constant Mean Curvature in Spheres
• Hypersurfaces with constant scalar curvature in space forms

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