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 The critical point equation on a four dimensional warped product manifold Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 679-692 Published online December 1, 2006 Seungsu Hwang and Jeongwook Chang Chung-Ang University, Kunsan National University Abstract : On a compact oriented $n$-dimensional manifold $(M^n,$ $g)$, it has been conjectured that a metric $g$ satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,g)$ is a $4$-dimensional oriented compact warped product, then $g$ can not be a solution of CPE with a non-zero solution function $f$. Keywords : critical point equation, warped product, Einstein metric MSC numbers : 53C25 Downloads: Full-text PDF