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A. Tayebi

Publications and source records attributed to A. Tayebi.

At least 19 recordsLinked to original sources
arXiv2026

On Berwald Spaces with non-Zero Flag Curvature

We prove that every Berwald manifold with non-zero flag curvature is Riemannian. This result provides an extension of Numata and Szabo's rigidity theorems. We show that every positively curved constant isotropic Berwald manifold is Riemannian or locally Minkowskian. Then, we prove that every compact strictly positive (or negative) isotropic Berwald manifold reduces to a Berwald manifold. Finally, we prove that every homogeneous isotropic Berwald metric is either locally Minkowskian, or Riemannian, or Berwald metric or Berwald-Randers metric generalizing result previously only known in the case of Randers metric.

math.DG↗
arXiv2021

On Non-Positively Curved Homogeneous Finsler Metrics

In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove that every connected homogeneous Finsler space with non-positive flag curvature and isotropic S-curvature is Riemannian or locally Minkowskian. We extend the Szabó's rigidity theorem for Berwald surfaces and show that homogeneous isotropic Berwald metrics with non-positive flag curvature are Riemannian or locally Minkowskian. We prove that a homogeneous $(α, β)$-metrics has isotropic mean Berwald curvature if and only if it has vanishing mean Berwald curvature generalizing result previously only known in the case of Randers metrics. Our second main result is to show that every homogeneous $(α,β)$-metric with non-positive flag curvature and almost isotropic S-curvature is Riemannian or locally Minkowskian.

math.DG↗
arXiv2019

Weighted Projective Ricci Curvature in Finsler Geometry

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

math.DG↗
arXiv2018

A Simple Proof for the Cycle Double Cover Conjecture

Given a bridgeless graph G, the well-known cycle double cover conjecture posits that there is a list of cycles of G, such that every edge appears in exactly two cycles. In this paper, we prove the cycle double cover conjecture. More precisely, we prove the Goddyn's conjecture as a stronger version of the cycle double cover conjecture which states that every cycle in G is a member of some cycle double cover of G.

math.CO↗
arXiv2015

Generalized P-Reducible $(α, β)$-Metrics with Vanishing S-curvature

In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called generalized P-reducible metrics that contains the class of P-reducible metrics. We prove that every generalized P-reducible $(α, β)$-metric with vanishing S-curvature reduces to a Berwald metric or C-reducible metric. It results that there is not any concrete P-reducible $(α,β)$-metric with vanishing S-curvature.

math.DG↗
arXiv2015

Matsumoto Metrics of Reversible Curvature

In this paper, we study the reversibility of Riemann curvature and Ricci curvature for the Matsumoto metric and prove three global results. First, we prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic. Then we show that a Matsumoto metric is Ricci-reversible if and only if it is Ricci-quadratic. Finally, we prove that every weakly Einstein Matsumoto metric is Ricci-reversible.

math.GM↗
arXiv2015

On Generalized Douglas-Weyl $(α, β)$-Metrics

In this paper, we study generalized Douglas-Weyl $(α, β)$-metrics. Suppose that an regular $(α, β)$-metric $F$ is not of Randers type. We prove that $F$ is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover by ignoring the regularity, if $F$ is not a Berwald metric then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.

math.DG↗
arXiv2015

Inertial Vector Based Attitude Stabilization of Rigid Body Without Angular Velocity Measurements

We address the problem of attitude stabilization of a rigid body, in which neither the angular velocity nor the instantaneous measurements of the attitude are used in the feedback, only body vector measurements are needed. The design of the controller is based on an angular velocity observer-like system, where a first order linear auxiliary system based directly on vector measurements is introduced. The introduction of gain matrices provides more tuning flexibility and better results compared with existing works. The proposed controller ensures almost global asymptotic stability. The performance and effectiveness of the proposed solution are illustrated via simulation results where the gains of the controller are adjusted using non linear optimization.

math.OC↗
arXiv2014

On Kropina Change of m-th Root Finsler Metrics

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.

math.DG↗
arXiv2014

On the Second Approximate Matsumoto Metric

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.

math.DG↗
arXiv2014

Some Results Related to Soft Topological Spaces

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft separation axioms that have been studied by Min and Shabir-Naz. By constructing a special soft topological space, show that some classical results in general topology are not true about soft topological spaces, for instance every compact Housdorff spaces need not be normal.

math.GM↗
arXiv2013

Quantum signal transmission through a single-qubit chain

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.

cond-mat.mes-hall↗
arXiv2013

Tensor sphere bundle of Cheeger-Gromoll type

We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundles endowed with the induced metric are never space forms.

math.DG↗
arXiv2013

Generalized P-Reducible Finsler Metrics

In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalize Matsumotos theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.

math.DG↗
arXiv2013

On phi-Recurrent Contact Metric Manifolds

In this paper, we prove that evry 3-dimensional manifold M is a ?- recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ?-recurrent contact metric manifolds of constant curvature. This implies that there exists no ?-recurrent N(k)-contact metric manifold, which is neither symmetric nor locally ?-symmetric.

math.DG↗