Taiwanese Journal of Mathematics

TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE

Gabjin Yun, Jeongwook Chang, and Seungsu Hwang

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Abstract

On a compact $n$-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved. In this paper, we prove that if the manifold with the critical point metric has harmonic curvature, then it is isometric to a standard sphere.

Article information

Source
Taiwanese J. Math., Volume 18, Number 5 (2014), 1439-1458.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706520

Digital Object Identifier
doi:10.11650/tjm.18.2014.1489

Mathematical Reviews number (MathSciNet)
MR3265071

Zentralblatt MATH identifier
1357.58017

Subjects
Primary: 58E11: Critical metrics 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
total scalar curvature critical point metric harmonic curvature Einstein metric

Citation

Yun, Gabjin; Chang, Jeongwook; Hwang, Seungsu. TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE. Taiwanese J. Math. 18 (2014), no. 5, 1439--1458. doi:10.11650/tjm.18.2014.1489. https://projecteuclid.org/euclid.twjm/1499706520


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References

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