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http://dx.doi.org/10.4134/BKMS.2013.50.4.1087

MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE  

Kim, Jongsu (Department of Mathematics Sogang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1087-1098 More about this Journal
Abstract
We find a $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on $\mathbb{R}^k$, $k{\geq}3$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^k$, the scalar curvatures of $g_t$ are strictly decreasing in $t$ in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball. Furthermore we extend the discussion to the Fubini-Study metric in a similar way.
Keywords
scalar curvature;
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Times Cited By KSCI : 2  (Citation Analysis)
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