Biharmonic properly immersed submanifolds in Euclidean spaces

Abstract

We consider a complete biharmonic immersed submanifold $M$ in an 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.

5 pages. arXiv admin note: text overlap with arXiv:1201.2872

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