Characterizations of linear Weingarten submanifolds

DOI10.1016/j.na.2017.09.003zbMath1384.53056OpenAlexW2764193146MaRDI QIDQ1675416

Fábio R. dos Santos, Henrique Fernandes de Lima

Publication date: 27 October 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2017.09.003

zbMATH Keywords

parallel normalized mean curvature vector fieldRiemannian space formscomplete linear Weingarten submanifolds

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20)

Related Items (3)

Gap theorems for linear Weingarten surfaces ⋮ LW-surfaces with higher codimension and Liebmann's theorem in the hyperbolic space ⋮ Sharp Simons type integral inequalities for closed linear Weingarten submanifolds in a space form

Cites Work

• Submanifolds with constant scalar curvature in a space form
• Submanifolds with constant scalar curvature in a unit sphere
• Complete hypersurfaces with constant scalar curvature in spheres
• A maximum principle for hypersurfaces with constant scalar curvature and applications
• On the scalar curvature of constant mean curvature hypersurfaces in space forms
• Global rigidity theorems of hypersurfaces
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Hypersurfaces with constant scalar curvature
• Submanifolds with parallel mean curvature vector in spheres
• A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds
• A new characterization of complete linear Weingarten hypersurfaces in real space forms
• Generalized maximum principles and the characterization of linear Weingarten hypersurfaces in space forms
• Isometric immersions of Riemannian manifolds
• Maximum Principles and Geometric Applications
• LINEAR WEINGARTEN HYPERSURFACES IN A UNIT SPHERE
• Harmonic functions on complete riemannian manifolds
• Submanifolds with Constant Mean Curvature
• Maximum principles on Riemannian manifolds and applications
• Submanifolds with constant scalar curvature
• Hypersurfaces of constant higher order mean curvature in warped products
• Hypersurfaces with constant scalar curvature in space forms

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