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http://dx.doi.org/10.4134/BKMS.2004.41.1.117

CRITICAL POINTS AND WARPED PRODUCT METRICS  

Hwang, Seung-Su (Department of Mathematics, Chung-Ang University)
Chang, Jeong-Wook (Department of Mathematics, Konkuk University)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 117-123 More about this Journal
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;
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