Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections

Abstract

In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that G1 and G7 do not have Codazzi tensors associated with Yano connections, G2, G3, G4, G5 and G6 have Codazzi tensors associated with Yano connections.

Keywords

• Codazzi tensors
• Yano connectoins
• Lorentzian Lie group