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  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd