Proper Biconservative immersions into the Euclidean space

2013/12/11 by Stefano Montaldo, Montaldo, Stefano, Cezar Oniciuc +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1312.3053

openalex publication_date 2013/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, using the framework of equivariant differential geometry, we study proper SO(p+1) × SO(q+1)-invariant biconservative hypersurfaces into the Euclidean space \mathbb Rⁿ (n=p+q+2) and proper SO(p+1)-invariant biconservative hypersurfaces into the Euclidean space \mathbb Rⁿ (n=p+2). Moreover, we show that, in these two classes of invariant families, there exists no proper biharmonic immersion.

Citations

• Harmonic Mappings of Riemannian Manifolds

Cited by

• Biconservative Weingarten surfaces with flat normal bundle in N⁴ (ε)
• Compact Biconservative Hypersurfaces in Space Forms: Rigidity Without Scalar Curvature Assumptions
• CMC biconservative surfaces in \mathbbSⁿ×ℝ and ℍⁿ×ℝ

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