arXiv subjects

A. Behzadi

Publications and source records attributed to A. Behzadi.

4 recordsLinked to original sources

arXiv2022

Geometry of submanifolds of all classes of third-order ODEs as a Riemannian manifold

In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs $y'''=f(x, y, p, q)$ as a Riemannian manifold where $y'=p$ and $y''=q$, if and only if $q_{yy}=0$. Moreover, we will see the linear second-order ODE with general form $y''=\pm y+β(x)$ is the only case that is defined a minimal surface and is also totally geodesic.

math.DG↗

arXiv2019

The equivalence between Finsler and non-commutative geometries by massive gravity black hole

In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of the system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent to the mentioned non-commutative Lagrangian under special conditions. Also, the effective potential of the system was calculated as a part of the corresponding conditions.

hep-th↗

arXiv2017

General $(α, β)$ metrics with relatively isotroic mean Landsberg curvature

In this paper, we study a new class of Finsler metrics, F=αϕ(b^2,s), s:=β/α, defined by a Riemannian metric αand 1-form β. It is called general (α, β) metric. In this paper, we assume ϕbe coefficient by s and βbe closed and conformal. We find a nessecary and sufficient condition for the metric of relatively isotropic mean Landsberg curvature to be Berwald.

math.DG↗

arXiv2017

On general $(α, β)$-metrics of weak Landsberg type

In this paper, we study general $(α,β)$-metrics which $α$ is a Riemannian metric and $β$ is an one-form. We have proven that every weak Landsberg general $(α,β)$-metric is a Berwald metric, where $β$ is a closed and conformal one-form. This show that there exist no generalized unicorn metric in this class of general $(α,β)$-metric. Further, We show that $F$ is a Landsberg general $(α,β)$-metric if and only if it is weak Landsberg general $(α,β)$-metric, where $β$ is a closed and conformal one-form.

math.MG↗