Biharmonic properly immersed submanifolds in Euclidean spaces |
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Authors: | Kazuo Akutagawa Shun Maeta |
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Institution: | 1. Division of Mathematics, GSIS, Tohoku University, Sendai, 980-8579, Japan
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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. |
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