Monatshefte für Mathematik

, Volume 177, Issue 4, pp 551–567 | Cite as

Triharmonic isometric immersions into a manifold of non-positively constant curvature

Article

Abstract

A triharmonic map is a critical point of the 3-energy in the space of smooth maps between two Riemannian manifolds. We study the generalized Chen’s conjecture for a triharmonic isometric immersion \(\varphi \) into a space form of non-positive constant curvature. We show that if the domain is complete and both the 4-energy of \(\varphi \), and the \(L^4\)-norm of the tension field \(\tau (\varphi )\), are finite, then such an immersion \(\varphi \) is minimal.

Keywords

Harmonic map Triharmonic map Chen’s conjecture Generalized Chen’s conjecture 

Mathematics Subject Classification

Primary 58E20 Secondary 53C43 

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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Shun Maeta
    • 1
  • Nobumitsu Nakauchi
    • 2
  • Hajime Urakawa
    • 3
  1. 1.Division of MathematicsShimane UniversityMatsueJapan
  2. 2.Graduate School of Science and EngineeringYamaguchi UniversityYamaguchiJapan
  3. 3.Institute for International EducationTohoku UniversitySendaiJapan

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