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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.

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Authors and Affiliations

  1. Division of Mathematics, GSIS, Tohoku University, Sendai, 980-8579, Japan

    Kazuo Akutagawa & Shun Maeta

Authors
  1. Kazuo Akutagawa
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  2. Shun Maeta
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Corresponding author

Correspondence to Shun Maeta.

Additional information

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.

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Akutagawa, K., Maeta, S. Biharmonic properly immersed submanifolds in Euclidean spaces. Geom Dedicata 164, 351–355 (2013). https://doi.org/10.1007/s10711-012-9778-1

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  • DOI: https://doi.org/10.1007/s10711-012-9778-1

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