Bull. Korean Math. Soc. 2012; 49(3): 581-588
Printed May 1, 2012
https://doi.org/10.4134/BKMS.2012.49.3.581
Copyright © The Korean Mathematical Society.
Yutae Kang, Jongsu Kim, and SeHo Kwak
Sogang University, Sogang University, Sogang University
We find a $C^{\infty}$ one-parameter family of Riemannian metrics $g_t$ on $\mathbb{R}^{3}$ for $0 \leq t \leq \varepsilon$ for some number $\varepsilon$ with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^{3}$, 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.
Keywords: scalar curvature
MSC numbers: 53B20, 53C20, 53C21
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