MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE

초록

We find a C-infinity-continuous path of Riemannian metrics g(t) on R-k, k >= 3, for 0 <= t <= epsilon for some number epsilon > 0 with the following property: g(0) is the Euclidean metric on R-k, the scalar curvatures of g(t) are strictly decreasing in t in the open unit ball and 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.

키워드