Osaka Journal of Mathematics

Biharmonic submanifolds in a Riemannian manifold

Norihito Koiso and Hajime Urakawa

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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

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

First available in Project Euclid: 18 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]


Koiso, Norihito; Urakawa, Hajime. Biharmonic submanifolds in a Riemannian manifold. Osaka J. Math. 55 (2018), no. 2, 325--346.

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