Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds
Yanlin Li, M. S. Siddesha, H. Aruna Kumara, M. M. Praveena
Abstract
In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω-connection with a parallel Cotton tensor is quasi-Einstein and Bach flat. Next, we show that any quasi-Einstein Lorentzian manifold admitting a semi-symmetric metric ω-connection is Bach flat.
Topics & Concepts
Characterization (materials science)Class (philosophy)Pure mathematicsMathematicsPhysicsComputer scienceArtificial intelligenceOpticsAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsAdvanced Neuroimaging Techniques and Applications