arXiv subjects

Amirhesam Zaeim

Publications and source records attributed to Amirhesam Zaeim.

3 recordsLinked to original sources

arXiv2025

Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group

In the framework of the study of homogeneous Lorentzian three-manifolds, we consider here the only class of examples which admit a four-dimensional group of isometries but are neither Lorentzian Bianchi-Cartan-Vranceanu spaces nor plane waves. We obtain an explicit description in global coordinates of these special homogeneous Lorentzian manifolds. We then prove that all such examples are non-gradient expanding Ricci solitons.

math.DG↗

arXiv2017

On symmetries of the Heisenberg group

We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields and their casual character. We also classify their Ricci, curvature and matter collineations, proving that there are no nontrivial examples.

math.DG↗

arXiv2016

Symmetries of Lorentzian Three-Manifolds with Recurrent Curvature

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter collineations, curvature and Weyl collineations. Several results are given for the broader class of three-dimensional Walker manifolds.

math.DG↗