Biminimal properly immersed submanifolds in the Euclidean spaces

We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper, that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we...

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Bibliographic Details
Published in:Journal of geometry and physics 2012-11, Vol.62 (11), p.2288-2293
Main Author: Maeta, Shun
Format: Article
Language:English
Subjects:
Biharmonic maps
Biharmonic submanifold
Chen’s conjecture
Minimal submanifold
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Summary:We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper, that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2012.07.006