On Ricci curvature of metric structures on g-manifolds

We study the properties of Ricci curvature of g-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation are investigated. In particular, sufficient conditions are found under which the g-manifold can be a Ricci soliton or a gradient Ricci soliton. Finally, we obtain a amazing (non-existence) higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of abelian g-manifolds. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study focuses on the Ricci curvature properties of g-manifolds, particularly in the case of higher dimensional abelian Lie algebras. It investigates the relationship between the Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation. Additionally, sufficient conditions for a g-manifold to be a Ricci soliton or gradient Ricci soliton are identified, and a surprising higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds is obtained for a special class of abelian g-manifolds.