Original Paper

Geometriae Dedicata

, Volume 164, Issue 1, pp 351-355

First online:

Biharmonic properly immersed submanifolds in Euclidean spaces

  • Kazuo AkutagawaAffiliated withDivision of Mathematics, GSIS, Tohoku University
  • , Shun MaetaAffiliated withDivision of Mathematics, GSIS, Tohoku University Email author 

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We consider a complete biharmonic immersed submanifold M in a Euclidean space \({\mathbb{E}^N}\). Assume that the immersion is proper, that is, the preimage of every compact set in \({\mathbb{E}^N}\) is also compact in M. Then, we prove that M is minimal. It is considered as an affirmative answer to the global version of Chen’s conjecture for biharmonic submanifolds.


Biharmonic map Biharmonic submanifold Chen’s conjecture

Mathematics Subject Classification (2010)

Primary: 58E20 Secondary: 53C43 53A07