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.

Gauss–Bonnet Theorem Related to the Semi-Symmetric Metric Connection in the Heisenberg Group

“…Proof. Based on similar discussions in [12][13][14][15][16][17][18], we assume that all points satisfy ω( γi (t)) ̸ = 0 and d dt (ω( γi (t))) ̸ = 0 on the curve γ i . Since our proof of Proposition 6 is based on the approximation argument relying on the Lebesgue Dominated Convergence Theorem, the finite sets are negligible.…”

“…According to the relevant studies described above, there is little research on the geometric properties related to semi-symmetric connections in the Heisenberg group. The research on the Gauss-Bonnet theorems related to different connections on between Lie groups can be found at the following references ( [12][13][14][15][16][17][18]). Under the influence of the above work, this paper attempts to research geometric properties related to the semi-symmetric connection in the Heisenberg group by employing the method of the Riemannian approximation scheme.…”