6 papers
Lorentzian Algebraic Ricci Solitons on the Heisenberg Group
Youssef Ayad
There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group , or equivalently, three nonequivalent Lorentzian inner products on the Heisenbe…
Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups
Youssef Ayad
In this paper, we compute the canonical and Kobayashi-Nomizu connections, together with their curvature, on Lorentzian four-dimensional nilpotent Lie groups endowed with a product…
Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups
Youssef Ayad
We investigate the conditions under which pseudo-Riemannian inner products induce pseudo-Riemannian algebraic Ricci solitons on four-dimensional Lie algebras. By analyzing the alge…
Isometry groups of simply connected nonunimodular Lie groups of dimension four
Youssef Ayad
For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.
Classification of left invariant Riemannian metrics on nonunimodular 4-dimensional Lie groups
Malika Ait Ben Haddou, Youssef Ayad
We classify, up to automorphism, left invariant Riemannian metrics on 4-dimensional simply connected nonunimodular Lie groups. This is equivalent to classifying, up to automorphism…
Isometry groups of simply connected unimodular 4-dimensional Lie groups
Youssef Ayad, Said Fahlaoui
We describe the full group of isometries of each left invariant Riemannian metric on the simply connected unimodular nilpotent or solvable -type Lie groups of dimension four.