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arXiv · 1106.3222

Biharmonic properly immersed submanifolds in Euclidean spaces

Kazuo Akutagawa·Shun Maeta
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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.

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Kazuo Akutagawa, Shun Maeta. 2012-08-21. Biharmonic properly immersed submanifolds in Euclidean spaces. https://arxiv.org/abs/1106.3222

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