Osaka Journal of Mathematics

Biharmonic submanifolds in a Riemannian manifold

Norihito Koiso and Hajime Urakawa

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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

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1524038731

Mathematical Reviews number (MathSciNet)
MR3787748

Zentralblatt MATH identifier
06870392

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

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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References

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