Codazzi tensors and the quasi-statistical structure associated to affine connections on three-dimensional Lorentzian Lie groups

TL;DR

This paper classifies three-dimensional Lorentzian Lie groups based on Ricci tensors and quasi-statistical structures related to various affine connections, advancing understanding of their geometric properties.

Contribution

It provides a comprehensive classification of Lorentzian Lie groups with Codazzi Ricci tensors and quasi-statistical structures linked to specific affine connections.

Findings

Classification of Lorentzian Lie groups with Codazzi Ricci tensors

Identification of groups with quasi-statistical structures

Insights into geometric structures associated with affine connections

Abstract

In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated to Bott connections, canonical connections and Kobayashi-Nomizu connections are Codazzi tensors associated to these connections. We also classify three-dimensional Lorentzian Lie group with the quasi-statistical structure associated to Bott connections, canonical connections and Kobayashi-Nomizu connections.