Geometriae Dedicata

, Volume 169, Issue 1, pp 263–272 | Cite as

Biharmonic maps into a Riemannian manifold of non-positive curvature

  • Nobumitsu Nakauchi
  • Hajime Urakawa
  • Sigmundur Gudmundsson
Original paper

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.

Keywords

Harmonic map Biharmonic map Chen’s conjecture   Generalized Chen’s conjecture 

Mathematics Subject Classification (2000)

Primary 58E20 Secondary 53C43 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Nobumitsu Nakauchi
    • 1
  • Hajime Urakawa
    • 2
    • 3
  • Sigmundur Gudmundsson
    • 4
  1. 1.Graduate School of Science and EngineeringYamaguchi UniversityYamaguchiJapan
  2. 2.Division of Mathematics, Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.Institute for International EducationTohoku UniversitySendaiJapan
  4. 4.Department of Mathematics, Faculty of ScienceLund UniversityLundSweden

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