Proper r-harmonic submanifolds into ellipsoids and rotation hypersurfaces
Montaldo, S.
;Ratto, A.
2018-01-01
Abstract
The study of r-harmonic maps was proposed by Eells–Sampson in 1965 and by Eells–Lemaire in 1983. These maps are a natural generalization of harmonic maps and are defined as the critical points of the r-energy functional Er(φ)=(1∕2)∫M|(d∗+d)r(φ)|2dvM, where φ:M→N denotes a smooth map between two Riemannian manifolds. If an r-harmonic map φ:M→N is an isometric immersion and it is not minimal, then we say that φ(M) is a proper r-harmonic submanifold of N. In this paper we prove the existence of several new, proper r-harmonic submanifolds into ellipsoids and rotation hypersurfaces.File | Size | Format | |
---|---|---|---|
Proper-r-harmonic-immersions.pdf open access
Description: Articolo principale
Type: versione post-print
Size 323.5 kB
Format Adobe PDF
|
323.5 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.