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Biharmonic maps into a Riemannian manifold of non-positive curvature

Nakauchi, Nobumitsu; Urakawa, Hajime and Gudmundsson, Sigmundur LU (2014) In Geometriae Dedicata 169. p.263-272
Abstract
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Harmonic map, Biharmonic map, Chen’s conjecture, Generalized Chen’s conjecture, Primary 58E20, Secondary 53C43
in
Geometriae Dedicata
volume
169
pages
263 - 272
publisher
Springer
external identifiers
  • wos:000332790500017
  • scopus:84897634404
ISSN
0046-5755
DOI
10.1007/s10711-013-9854-1
language
English
LU publication?
yes
id
b6bb01d6-815b-47ab-b918-8ea78a56e710 (old id 2628638)
date added to LUP
2013-09-23 13:18:09
date last changed
2019-01-06 05:08:14
@article{b6bb01d6-815b-47ab-b918-8ea78a56e710,
  abstract     = {We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.},
  author       = {Nakauchi, Nobumitsu and Urakawa, Hajime and Gudmundsson, Sigmundur},
  issn         = {0046-5755},
  keyword      = {Harmonic map,Biharmonic map,Chen’s conjecture,Generalized Chen’s conjecture,Primary 58E20,Secondary 53C43},
  language     = {eng},
  pages        = {263--272},
  publisher    = {Springer},
  series       = {Geometriae Dedicata},
  title        = {Biharmonic maps into a Riemannian manifold of non-positive curvature},
  url          = {http://dx.doi.org/10.1007/s10711-013-9854-1},
  volume       = {169},
  year         = {2014},
}