Biharmonic properly immersed submanifolds in Euclidean spaces

By K. Akutagawa, S. Maeta. 2011

89 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d1a5bebd5f419001332a14bb4cf84da8f299cd5d

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In Applied Mathematics

1. Bang‐Yen Chen
2. Ion Mihai
3. Bayram Sahin
4. I. Hasegawa
5. Siraj Uddin

In Geometry and Topology

1. Bang‐Yen Chen
2. Ion Mihai
3. I. Hasegawa

Citations in the corpus

• Some open problems and conjectures on submanifolds of finite type: recent development (2014, background): “The global version of my original biharmonic conjecture can be found, for instance, in [1, 140].”