, Volume 164, Issue 1, pp 351-355
Date: 02 Sep 2012

Biharmonic properly immersed submanifolds in Euclidean spaces

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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.

K. Akutagawa was supported in part by Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, No. 24340008.
S. Maeta was supported in part by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists, No. 23-6949.