New examples of \(r\)-harmonic immersions into the sphere

DOI10.1016/j.jmaa.2017.09.046zbMath1377.53083arXiv1611.09001OpenAlexW2557244496MaRDI QIDQ1674433

Andrea Ratto, Stefano Montaldo

Publication date: 2 November 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09001

zbMATH Keywords

harmonic maps\(r\)-harmonic maps and submanifolds

Mathematics Subject Classification ID

Global submanifolds (53C40) Differential geometric aspects of harmonic maps (53C43)

Related Items (17)

Unique continuation properties for polyharmonic maps between Riemannian manifolds ⋮ Higher order energy functionals and the Chen-Maeta conjecture ⋮ A note on biharmonic functions on the Thurston geometries ⋮ Triharmonic CMC hypersurfaces in space forms with at most \(3\) distinct principal curvatures ⋮ Polyharmonic hypersurfaces into space forms ⋮ Triharmonic CMC hypersurfaces in \({\mathbb{R}}^5(c)\) ⋮ Some classifications of conformal biharmonic and \(k\)-polyharmonic maps ⋮ Higher order energy functionals ⋮ On the normal stability of triharmonic hypersurfaces in space forms ⋮ Triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms ⋮ On triharmonic hypersurfaces in space forms ⋮ A classification of triharmonic hypersurfaces in a pseudo-Riemannian space form ⋮ Polyharmonic hypersurfaces into pseudo-Riemannian space forms ⋮ On polyharmonic helices in space forms ⋮ A structure theorem for polyharmonic maps between Riemannian manifolds ⋮ Proper \(r\)-harmonic submanifolds into ellipsoids and rotation hypersurfaces ⋮ The stress-energy tensor for polyharmonic maps

Cites Work

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• Harmonic Maps and Minimal Immersions with Symmetries (AM-130)
• Another Report on Harmonic Maps
• Polyharmonic maps into the Euclidean space
• $k$-harmonic maps into a Riemannian manifold with constant sectional curvature

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