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Bull. Korean Math. Soc. 2006; 43(4): 679-692
Printed December 1, 2006
Copyright © The Korean Mathematical Society.
The critical point equation on a four dimensional warped product manifold
Seungsu Hwang and Jeongwook Chang
Chung-Ang University, Kunsan National University
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
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