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CRITICAL POINTS AND WARPED PRODUCT METRICS

  • Hwang, Seung-Su (Department of Mathematics, Chung-Ang University) ;
  • Chang, Jeong-Wook (Department of Mathematics, Konkuk University)
  • Published : 2004.02.01

Abstract

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

Keywords

total scalar curvature functional;critical point equation;Einstein metric

References

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Cited by

  1. A note on static spaces and related problems vol.74, 2013, https://doi.org/10.1016/j.geomphys.2013.07.003
  2. CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.655