\(C^\infty\) compactness for a class of Riemannian manifolds with parallel Ricci curvature (Q2739138)

The authors study some properties of a set of closed Riemannian manifolds with parallel Ricci curvature, with lower bounds for sectional curvature and a upper bound for the volume. NEWLINENEWLINENEWLINEThey prove that such class of manifolds are analytic and compact in Gromov-Hausdorff topology. They also prove that, under certain specified conditions, a Ricci flat manifold (of this class) is flat.