Taiwanese Journal of Mathematics


Gabjin Yun, Jeongwook Chang, and Seungsu Hwang

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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

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

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

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

total scalar curvature critical point metric harmonic curvature Einstein metric


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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