Bulletin of the Korean Mathematical Society ( Vol.43 NO.4 / 2006 ) Title The critical point equation on a four dimensional warped product manifold(ENG) Author Seungsu Hwang ,Jeongwook Chang  MSC 53C25 Publication Page 679-692 Page Abstract 1. Introduction 2. Preliminaries 3. Proof of main theorem 4. Proof of Lemma 5. A rigidity result Own Status Keyword critical point equation, warped product, Einstein metric Note Summary 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 $f$. Attach [DVI]  [PDF]