Stability of the L^p-Norm of the Curvature Tensor at Kahler Space Forms

Abstract

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by $R_p(g):={\int }_M|R(g){|}^{p}dvg$ where $R(g)$, $d{v}_g$ denote the corresponding Riemannian curvature, volume form and p is a real number greater than or equal to 2. We prove that $R_p$ restricted to the space of Kahler metrics attains its local minima at a metric with constant holomorphic sectional curvature.

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