Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Three dimensional critical point of the total scalar curvature

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

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