Polyharmonic, or r-harmonic, maps are a natural generalization of harmonic maps whose study was proposed by EellsâLemaire 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:Snâ1(R)âªSnis a proper r-harmonic submanifold of Snif 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.
New examples of r-harmonic immersions into the sphere
Montaldo, S.;Ratto, A.
2018-01-01
Abstract
Polyharmonic, or r-harmonic, maps are a natural generalization of harmonic maps whose study was proposed by EellsâLemaire 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:Snâ1(R)âªSnis a proper r-harmonic submanifold of Snif 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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