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 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:Sn−1(R)↪Snis 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.
2018
Harmonic maps; r-Harmonic maps and submanifolds; Analysis; Applied mathematics
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