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Hamid Reza Salimi Moghaddam

Publications and source records attributed to Hamid Reza Salimi Moghaddam.

25 records · Page 2Linked to original sources
arXiv2016

Left Invariant Randers Metrics of Berwald type on Tangent Lie Groups

Let $G$ be a Lie group equipped with a left invariant Randers metric of Berward type $F$, with underlying left invariant Riemannian metric $g$. Suppose that $\widetilde{F}$ and $\widetilde{g}$ are lifted Randers and Riemannian metrics arising from $F$ and $g$ on the tangent Lie group $TG$ by vertical and complete lifts. In this article we study the relations between the flag curvature of the Randers manifold $(TG,\widetilde{F})$ and the sectional curvature of the Riemannian manifold $(G,g)$ when $\widetilde{F}$ is of Berwald type. Then we give all simply connected $3$-dimentional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.

math.DG↗
arXiv2016

Riemannian Geometry of Two Families of Tangent Lie Groups

Using vertical and complete lifts, any left invariant Riemannian metric on a Lie group induces a left invariant Riemannian metric on the tangent Lie group. In the present article we study the Riemannian geometry of tangent bundle of two families of Lie groups. The first one is the family of special Lie groups considered by J. Milnor and the second one is the class of Lie groups with one-dimensional commutator groups. The Levi-Civita connection, sectional and Ricci curvatures have been investigated.

math.DG↗
arXiv2013

Geodesic Vector fields of invariant $(α,β)$-metrics on Homogeneous spaces

In this paper we show that for an invariant $(α,β)-$metric $F$ on a homogeneous Finsler manifold $\frac{G}{H}$, induced by an invariant Riemannian metric $\tilde{a}$ and an invariant vector field $\tilde{X}$, the vector $X=\tilde{X}(H)$ is a geodesic vector of $F$ if and only if it is a geodesic vector of $\tilde{a}$. Then we give some conditions such that under them, an arbitrary vector is a geodesic vector of $F$ if and only if it is a geodesic vector of $\tilde{a}$. Finally we give an explicit formula for the flag curvature of bi-invariant $(α,β)-$metrics on connected Lie groups.

math.DG↗
arXiv2013

Two new families of Finsler connections on even-dimensional manifolds

Let $F^{2n}=(M,M',F^{\ast})$ be an even-dimensional pseudo-Finsler manifold. We construct an almost hypercomplex structure on any chart domain of a certain atlas of $M'$ by using a considered non-linear connection. Then by using the almost hypercomplex structure we define two new families of Finsler connections. Also we show that for any Finsler connection $\nabla$ there exists a linear connection $D$ such that the local almost hypercomplex structure is parallel with respect to it.

math.DG↗
arXiv2013

Symplectic Connections Induced by the Chern Connection

Let $(M,ω)$ be a symplectic manifold and $F$ be a Finsler structure on $M$. In the present paper we define a lift of the symplectic two-form $ω$ on the manifold $TM\backslash 0$, and find the conditions that the Chern connection of the Finsler structure $F$ preserves this lift of $ω$. In this situation if $M$ admits a nowhere zero vector field then we have a non-empty family of Fedosov structures on $M$.

math.DG↗
arXiv2006

The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections

In the present paper, the $(HM',S,T)$-Cartan connections on pseudo-Finsler manifolds, introduced by A. Bejancu and H.R. Farran, are obtained by the natural almost complex structure arising from the nonlinear connection $HM'$. We prove that the natural almost complex linear connection associated to a $(HM',S,T)$-Cartan connection is a metric linear connection with respect to the Sasaki metric $G$. Finally we give some conditions for $(M', J, G)$ to be a Kähler manifold.

math.DG↗