%0 Journal Article
%T On the spectral geometry of 4-dimensional Lorentzian Lie group
%J Journal of Finsler Geometry and its Applications
%I University of Mohaghegh Ardabili
%Z 2783-0500
%A Seifipour, Davood
%D 2022
%\ 12/01/2022
%V 3
%N 2
%P 99-118
%! On the spectral geometry of 4-dimensional Lorentzian Lie group
%K Codazzi space
%K statistical manifold
%K Lie group
%R 10.22098/jfga.2022.11917.1080
%X The main focus of this paper is concern to the study on the point-wise Osserman structure on 4-dimensional Lorentzian Lie group. In this paper we study on the spectrum of the Jacobi operator and spectrum of the skew-symmetric curvature operator on the non-abelian 4-dimensional Lie group G, whenever G equipped with an orthonormal left invariant pseudo-Riemannian metric g of signature (-;+;+; +), i.e, Lorentzian metric, where e1 is a unit time-like vector. The Lie algebra structure in dimension four has key role in our investigation, also in this case we study on the classification of 1-Stein and mixed IP spaces. At the end we show that G does not admit any space form and Einstein structures.
%U https://jfga.uma.ac.ir/article_1959_92e7e83227cf41270eda835cd043db35.pdf