MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE

Title & Authors
MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE
Kim, Jongsu;

Abstract
We find a $\small{C^{\infty}}$-continuous path of Riemannian metrics $\small{g_t}$ on $\small{\mathbb{R}^k}$, $\small{k{\geq}3}$, for $\small{0{\leq}t{\leq}{\varepsilon}}$ for some number $\small{{\varepsilon}}$ > 0 with the following property: $\small{g_0}$ is the Euclidean metric on $\small{\mathbb{R}^k}$, the scalar curvatures of $\small{g_t}$ are strictly decreasing in $\small{t}$ in the open unit ball and $\small{g_t}$ is isometric to the Euclidean metric in the complement of the ball. Furthermore we extend the discussion to the Fubini-Study metric in a similar way.
Keywords
scalar curvature;
Language
English
Cited by
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A NOTE ON DECREASING SCALAR CURVATURE FROM FLAT METRICS,;

호남수학학술지, 2013. vol.35. 4, pp.647-655
2.
SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC,;;

한국수학교육학회지시리즈B:순수및응용수학, 2013. vol.20. 4, pp.269-276
1.
Smooth scalar curvature decrease of big scale on a sphere, Differential Geometry and its Applications, 2014, 37, 120
2.
A NOTE ON DECREASING SCALAR CURVATURE FROM FLAT METRICS, Honam Mathematical Journal, 2013, 35, 4, 647
3.
SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC, The Pure and Applied Mathematics, 2013, 20, 4, 269
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