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Biminimal properly immersed submanifolds in the Euclidean spaces

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Volume
62
Issue
11
Identifiers
DOI: 10.1016/j.geomphys.2012.07.006
Keywords
  • Biharmonic Maps
  • Chen’S Conjecture
  • Biharmonic Submanifold
  • Minimal Submanifold

Abstract

Abstract 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<0, we construct examples of biminimal submanifolds and curves.

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