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Canonical connections and algebraic Wanas solitons of three-dimensional Lorentzian Lie groups

Yong Wang, Yue Tang

Abstract

In this paper, we compute the Wanas tensor associated to canonical connections on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Wanas solitons associated to canonical connections. We classify algebraic Wanas solitons associated to canonical connections on three-dimensional Lorentzian Lie groups with some product structure.

Canonical connections and algebraic Wanas solitons of three-dimensional Lorentzian Lie groups

Abstract

In this paper, we compute the Wanas tensor associated to canonical connections on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Wanas solitons associated to canonical connections. We classify algebraic Wanas solitons associated to canonical connections on three-dimensional Lorentzian Lie groups with some product structure.

Paper Structure

This paper contains 4 sections, 26 theorems, 128 equations.

Table of Contents

  1. Introduction
  2. Algebraic Wanas solitons associated to canonical connections on three-dimensional unimodular Lorentzian Lie groups
  3. Algebraic Wanas solitons associated to canonical connections on three-dimensional non-unimodular Lorentzian Lie groups
  4. Acknowledgements

Key Result

Lemma 2.2

The canonical connection $\nabla^0$ of $(G_1,J)$ is given by

Theorems & Definitions (31)

  • Definition 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Lemma 2.6
  • Lemma 2.7
  • Theorem 2.8
  • proof
  • Theorem 2.9
  • ...and 21 more