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ISSN : 1226-0657
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SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC
SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC
Kim, Jongsu (Department of Mathematics, Sogang University)
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
참고문헌
(2005). KIDs are non-generic. Ann. Henri Poincare, 6, 155-194. 10.1007/s00023-005-0202-3.
Einstein manifolds;Ergebnisse der Mathematik, 3 Folge, Band 10.
(2000). Scalar curvature deformation and a gluing construction for the Einstein constraint equations. Comm. Math. Phys., 214, 137-189. 10.1007/PL00005533.
Kang, Yu-Tae;Kim, Jong-Su;Kwak, Se-Ho;. (2012). MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION. Bulletin of the Korean Mathematical Society, 49(3), 581-588. 10.4134/BKMS.2012.49.3.581.
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.
(1995). Curvature h-principles. Ann. of Math., 142(2), 457-498. 10.2307/2118552.
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