Critical points and warped product metrics

초록

It has been conjectured that, on a compact orientable manifoldM, a critical point of the total scalar curvature functionalrestricted the space of unit volume metrics of constant scalarcurvature is Einstein. In this paper we show that if a manifold isa 3-dimensional warped product, then (M,g) cannot be acritical point unless it is isometric to the standard sphere.

키워드