Symmetries of four-dimensional Lorentzian Damek-Ricci spaces

Authors

  • A. Mostefaoui École Nationale Polytechnique d'Oran-Maurice Audin, Algeria
  • N. Sidhoumi École Nationale Polytechnique d'Oran-Maurice Audin, Algeria

DOI:

https://doi.org/10.31926/but.mif.2021.1.63.1.13

Keywords:

Damek-Ricci spaces, Killing vector fields, affine vector fields, Lorentzian metrics, left-invariant metrics, curvature collineation, matter collineation

Abstract

We consider the four-dimensional Damek-Ricci spaces, equipped with the left-invariant Lorentzian metric. We obtain a full classifiction of Killing and affine vector fields as well as Ricci, curvature, and matter collineations. In particular, we prove the non-existence of proper (that is non Killing) affine vector field.

Author Biographies

A. Mostefaoui, École Nationale Polytechnique d'Oran-Maurice Audin, Algeria

B.P 1523 El M'naouar Oran 31000

N. Sidhoumi, École Nationale Polytechnique d'Oran-Maurice Audin, Algeria

B.P 1523 El M'naouar Oran 31000

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Published

2021-07-08

Issue

Vol. 1(63) No. 1 (2021)

Section

MATHEMATICS