arXiv subjects
Publications and source records attributed to Mohammed Guediri.
The main purpose of this paper is to show that a normalized non-steady gradient Ricci soliton (M,g,f,λ) of dimension n is trivial if and only if its scalar curvature S satisfies the equality S=λ(f+(n/2)).
In this paper, we shall use a method based on the theory of extensions of left-symmetric algebras to classify complete left-invariant affine real structures on solvable non-unimodular three-dimensional Lie groups.
We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the identity [x,y].z=0. We derive some basic characterizations of such left-symmetric algebras and we highlight their relationships with the so-called Novikov algebras and derivation algebras.
The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the oscillator group.