Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds

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.

Keywords

• Bach tensor
• Cotton tensor
• Lorentzian manifolds
• semi-symmetric metric connection