On Holonomy Algebras of Four-Dimensional Generalized Quasi-Einstein Manifolds

Abstract

Generalized quasi-Einstein manifolds on 4-dimensional manifolds admitting a metric whose signature is one of the only possibilities (+,+,-,-), (+,+,+,-) are based on the holonomy group of the Levi-Civita connection associated with the metric.By considering the possible Lie algebras which are known for all signatures, the holonomy types permitting generalized quasi-Einstein manifolds are determined using some computational methods and the Ambrose-Singer theorem.