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 Three dimensional critical point of the total scalar curvature Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 867-871 https://doi.org/10.4134/BKMS.2013.50.3.867Printed May 31, 2013 Seungsu Hwang Chung-Ang University Abstract : 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 Downloads: Full-text PDF