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ISSN : 1226-0657

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Vol.20 No.4

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SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.4, pp.269-276
https://doi.org/10.7468/jksmeb.2013.20.4.269
Kang, Yutae
Kim, Jongsu
Kang,, Y. , & Kim,, J. (2013). SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(4), 269-276, https://doi.org/10.7468/jksmeb.2013.20.4.269

Abstract

We find an explicit <TEX>$C^{\infty}$</TEX>-continuous path of Riemannian metrics <TEX>$g_t$</TEX> on the 4-d hyperbolic space <TEX>$\mathbb{H}^4$</TEX>, for <TEX>$0{\leq}t{\leq}{\varepsilon}$</TEX> for some number <TEX>${\varepsilon}$</TEX> > 0 with the following property: <TEX>$g_0$</TEX> is the hyperbolic metric on <TEX>$\mathbb{H}^4$</TEX>, the scalar curvatures of <TEX>$g_t$</TEX> are strictly decreasing in t in an open ball and <TEX>$g_t$</TEX> is isometric to the hyperbolic metric in the complement of the ball.

keywords
scalar curvature decrease, scalar curvature functional

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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