A-manifolds on a principal torus bundle over an almost Hodge A-manifold base

Abstract

An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇ X Ric(X, X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds.