On cohomogeneity one biharmonic hypersurfaces into the Euclidean space

DOI10.1016/J.GEOMPHYS.2016.04.012zbMath1341.53010arXiv1507.03964OpenAlexW1961707989MaRDI QIDQ295777

Andrea Ratto, Cezar Dumitru Oniciuc, Stefano Montaldo

Publication date: 13 June 2016

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03964

zbMATH Keywords

transformation groupsbiharmonic mapsequivariant differential geometrybiharmonic immersionscohomogeneity one hypersurfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Harmonic maps, etc. (58E20)

Related Items (8)

Higher order energy functionals and the Chen-Maeta conjecture ⋮ Some recent progress of biharmonic submanifolds ⋮ Triharmonic CMC hypersurfaces in space forms with at most \(3\) distinct principal curvatures ⋮ Polyharmonic hypersurfaces into space forms ⋮ Recent progress of biharmonic hypersurfaces in space forms ⋮ Biharmonic conjectures on hypersurfaces in a space form ⋮ Biharmonic hypersurfaces with constant scalar curvature in space forms ⋮ On Chen's biharmonic conjecture for hypersurfaces in \(\mathbb{R}^5\)

Cites Work

• Proper biconservative immersions into the Euclidean space
• Biharmonic PNMC submanifolds in spheres
• Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean 5-space
• Biharmonic hypersurfaces in Riemannian manifolds
• Isoparametrische Hyperflächen in Sphären. I
• Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces. I
• Biharmonic properly immersed submanifolds in Euclidean spaces
• Biharmonic maps into a Riemannian manifold of non-positive curvature
• Minimal cones and the Bernstein problem
• Minimal submanifolds of low cohomogeneity
• Total Mean Curvature and Submanifolds of Finite Type
• Harmonic Maps and Minimal Immersions with Symmetries (AM-130)
• BIMINIMAL IMMERSIONS
• Hypersurfaces of E4 with Harmonic Mean Curvature Vector
• Hypersurfaces in E⁴ with Harmonic Mean Curvature Vector Field
• Recent developments of biharmonic conjecture and modified biharmonic conjectures
• Harmonic Mappings of Riemannian Manifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On cohomogeneity one biharmonic hypersurfaces into the Euclidean space