## Osaka Journal of Mathematics

### Biharmonic submanifolds in a Riemannian manifold

#### Abstract

In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.

#### Article information

Source
Osaka J. Math., Volume 55, Number 2 (2018), 325-346.

Dates
First available in Project Euclid: 18 April 2018

https://projecteuclid.org/euclid.ojm/1524038731

Mathematical Reviews number (MathSciNet)
MR3787748

Zentralblatt MATH identifier
06870392

#### Citation

Koiso, Norihito; Urakawa, Hajime. Biharmonic submanifolds in a Riemannian manifold. Osaka J. Math. 55 (2018), no. 2, 325--346. https://projecteuclid.org/euclid.ojm/1524038731

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