Geometriae Dedicata

, Volume 164, Issue 1, pp 351–355

Biharmonic properly immersed submanifolds in Euclidean spaces

Authors

  • Kazuo Akutagawa
    • Division of Mathematics, GSISTohoku University
    • Division of Mathematics, GSISTohoku University
Original Paper

DOI: 10.1007/s10711-012-9778-1

Cite this article as:
Akutagawa, K. & Maeta, S. Geom Dedicata (2013) 164: 351. doi:10.1007/s10711-012-9778-1

Abstract

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.

Keywords

Biharmonic map Biharmonic submanifold Chen’s conjecture

Mathematics Subject Classification (2010)

Primary: 58E20 Secondary: 53C43 53A07

Copyright information

© Springer Science+Business Media B.V. 2012