Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION

  • Received : 2011.02.04
  • Published : 2012.05.31
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Abstract

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.

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References

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Cited by

  1. MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1087
  2. SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC vol.20, pp.4, 2013, https://doi.org/10.7468/jksmeb.2013.20.4.269