Esmaeil Peyghan

The purpose of this paper is to introduce Hom-alternative rings, Hom-Lie rings and Hom-Jordan rings. We study some of their properties and provide construction procedures using ordinary alternative rings or Lie rings or Jordan rings. Also, we show that a polarization of Hom-associative ring leads to Hom-Lie ring or Hom-Jordan ring.

One of the classical fundamental motifs in differential geometry of manifolds is the notion of the almost contact structure. As a counterpart of the almost contact metric structure, the notion of the almost contact B-metric structure has been an interesting research field for many mathematicians in differential geometry of manifolds, and ...

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $\beta$-change of an m-th root metric be locally dually flat. Finally, we prove that the conformal $\beta$-change of locally projectively flat m-th root metrics are locally Minkowskian.

The paper considers a class of g-natural metrics G on the tangent bundle TM of a Riemannian manifold (M, g). We prove that the flatness of g is necessary and sufficient for a metric G to be weakly symmetric (recurrent or pseudo-symmetric). Also, it is shown that the weak symmetry and recurrent or pseudo-symmetry properties of Sasakian lift metric, studied by Bejan and Crasmareanu, and Binh and Tamássy, respectively, are special cases of our result.

In this paper, we consider locally dually flat Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We find some conditions under which such a Finsler metric is Berwaldian, Riemannian or locally Minkowskian.

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.

In this paper, we study the second approximate Matsumoto metric on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

Considering the class G of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g), it is shown that the flatnees for g is a necessary and sufficient condition of weakly symmetry (recurrent or pseudo-symmetry) of G. In particular, the cases of weakly symmetric Sasakian lift metric studied by Bejan and Crasmareanu and recurrent or pseudo-symmetric Sasakian lift metric studied by Binh and Tamassy are obtained.