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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 20(4), 269-276, https://doi.org/10.7468/jksmeb.2013.20.4.269

Abstract

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

keywords
scalar curvature decrease, scalar curvature functional

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Kim, Jongsu;. (2013). MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE. Bulletin of the Korean Mathematical Society, 50(4), 1087-1098. 10.4134/BKMS.2013.50.4.1087.

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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