Biharmonic properly immersed submanifolds in the Euclidean spaces

Details Biharmonic properly immersed submanifolds in the Euclidean spaces Biharmonic properly immersed submanifolds in the Euclidean spaces

2011-06-16

arxiv.org/abs/1106.3222v2

Mathematics

Differential Geometry

5 pages

Scientific paper

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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