MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION

Title & Authors
MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION
Kang, Yu-Tae; Kim, Jong-Su; Kwak, Se-Ho;

Abstract
We find a $\small{C^{\infty}}$ one-parameter family of Riemannian metrics $\small{g_t}$ on $\small{\mathbb{R}^3}$ for $\small{0{\leq}t{\leq}{\varepsilon}}$ for some number $\small{{\varepsilon}}$ with the following property: $\small{g_0}$ is the Euclidean metric on $\small{\mathbb{R}^3}$, the scalar curvatures of $\small{g_t}$ are strictly decreasing in t in the open unit ball and $\small{g_t}$ is isometric to the Euclidean metric in the complement of the ball.
Keywords
scalar curvature;
Language
English
Cited by
1.
MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE,;

대한수학회보, 2013. vol.50. 4, pp.1087-1098
2.
SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC,;;

한국수학교육학회지시리즈B:순수및응용수학, 2013. vol.20. 4, pp.269-276
1.
MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1087
2.
SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC, The Pure and Applied Mathematics, 2013, 20, 4, 269
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