Bull. Korean Math. Soc. 2013; 50(3): 867-871
Printed May 31, 2013
https://doi.org/10.4134/BKMS.2013.50.3.867
Copyright © The Korean Mathematical Society.
Seungsu Hwang
Chung-Ang University
It has been conjectured that, on a compact $3$-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that $\ker s_g'^*\neq 0$, which generalizes the previous partial results.
Keywords: total scalar curvature, critical point metric, Einstein metric
MSC numbers: Primary 53C25
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