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

Biharmonic properly immersed submanifolds in Euclidean spaces

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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.