Hokkaido Mathematical Journal

Rigidity of transversally biharmonic maps between foliated Riemannian manifolds

Shinji OHNO, Takashi SAKAI, and Hajime URAKAWA

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Abstract

On a smooth foliated map from a complete, possibly non-compact, foliated Riemannian manifold into another foliated Riemannian manifold of which transversal sectional curvature is non-positive, we will show that, if it is transversally biharmonic and has the finite energy and finite bienergy, then it is transversally harmonic.

Article information

Source
Hokkaido Math. J., Volume 47, Number 3 (2018), 637-654.

Dates
First available in Project Euclid: 26 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1537948835

Digital Object Identifier
doi:10.14492/hokmj/1537948835

Mathematical Reviews number (MathSciNet)
MR3858383

Zentralblatt MATH identifier
06959108

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

Keywords
foliation divergence theorem transversally harmonic transversally biharmonic

Citation

OHNO, Shinji; SAKAI, Takashi; URAKAWA, Hajime. Rigidity of transversally biharmonic maps between foliated Riemannian manifolds. Hokkaido Math. J. 47 (2018), no. 3, 637--654. doi:10.14492/hokmj/1537948835. https://projecteuclid.org/euclid.hokmj/1537948835


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