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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2020; 57(2): 523-537

Online first article August 23, 2019      Printed March 1, 2020

https://doi.org/10.4134/JKMS.j190198

Copyright © The Korean Mathematical Society.

On the symmetries of the $Sol_{3}$ Lie group

Lakehal Belarbi

University of Mostaganem (U.M.A.B.)

Abstract

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In this work we consider the $Sol_{3}$ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.

Keywords: Lorentzian $Sol_{3}$ group, Killing vector fields, affine vector fields, Ricci collineations, curvature collineations, matter collineations

MSC numbers: 53C50, 53B30

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