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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
New-examples-r-harmonic-immersions-into-spheres-arxiv.pdf
Solo gestori archivio
Tipologia:
versione post-print
Dimensione
312.15 kB
Formato
Adobe PDF
|
312.15 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
