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Left-invariant Codazzi tensors and harmonic curvature on Lie groups endowed with a left invariant Lorentzian metric
- Publication Year :
- 2024
-
Abstract
- A Lorentzian Lie group is a Lie group endowed with a left invariant Lorentzian metric. We study left-invariant Codazzi tensors on Lorentzian Lie groups. We obtain new results on left-invariant Lorentzian metrics with harmonic curvature and non-parallel Ricci operator. In contrast to the Riemannian case, the Ricci operator of a let-invariant Lorentzian metric can be of four types: diagonal, of type $\{n-2,z\bar{z}\}$, of type $\{n,a2\}$ and of type $\{n,a3\}$. We first describe Lorentzian Lie algebras with a non-diagonal Codazzi operator and with these descriptions in mind, we study three classes of Lorentzian Lie groups with harmonic curvature. Namely, we give a complete description of the Lie algebra of Lorentzian Lie groups having harmonic curvature and where the Ricci operator is non-diagonal and its diagonal part consists of one real eigenvalue $\alpha$.<br />Comment: 50 pages, submitted
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.16381
- Document Type :
- Working Paper