Polyharmonic maps into the Euclidean space

doi:10.1285/i15900932v38n1p89

Polyharmonic maps into the Euclidean space

Nobumitsu Nakauchi, Hajime Urakawa

Abstract

We study polyharmonic ( $k$ -harmonic) maps between Riemannian manifolds with finite $j$ -energies $(j=1,\cdots,2k-2)$ . We show that if the domain is complete and the target is the Euclidean space, then such a map is harmonic.

DOI Code: 10.1285/i15900932v38n1p89

Keywords: harmonic map; polyharmonic map; Chen's conjecture; generalized Chen's conjecture

Full Text: PDF

This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.

Username
Password
Remember me

Note di Matematica

Polyharmonic maps into the Euclidean space

Abstract