New examples of r-harmonic immersions into the sphere

2016/11/28 by Stefano Montaldo, Montaldo, Stefano, Andrea Ratto +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1611.09001

openalex publication_date 2016/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Polyharmonic, or r-harmonic, maps are a natural generalization of harmonic maps whose study was proposed by Eells-Lemaire in 1983. The main aim of this paper is to construct new examples of proper r-harmonic immersions into spheres. In particular, we shall prove that the canonical inclusion i: S^n-1(R)→ Sⁿ is a proper r-harmonic submanifold of Sⁿ if and only if the radius R is equal to 1/ √(r). We shall also prove the existence of proper r-harmonic generalized Clifford's tori into the sphere.

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