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THE CRITICAL POINT EQUATION ON A FOUR DIMENSIONAL WARPED PRODUCT MANIFOLD

  • Hwang, Seung-Su (DEPARTMENT OF MATHEMATICS, CHUNG-ANG UNIVERSITY) ;
  • Chang, Jeong-Wook (DEPARTMENT OF MATHEMATICS, SCHOOL OF MATHEMATICS INFORMATICS AND STATISTICS, KUNSAN NATIONAL UNIVERSITY)
  • Published : 2006.11.30

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.

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Cited by

  1. CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.655