TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES

초록

On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker s∗g≠0 and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

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