arXiv subjects

Guojun Yang

Publications and source records attributed to Guojun Yang.

At least 19 recordsLinked to original sources

arXiv2023

On Geodesics of Sprays and Projective Completeness

Geodesics, which play an important role in spray-Finsler geometry, are integral curves of a spray vector field on a manifold. Some comparison theorems and rigidity issues are established on the completeness of geodesics of a spray or a Finsler metric. In this paper, projectively flat sprays with weak Ricci constant (eps. constant curvature) are classified at the level of geodesics. Further, a geodesic method is introduced to determine an $n$-dimensional spray based on a family of curves with $2(n-1)$ free constant parameters as geodesics. Finally, it shows that a spray is projectively complete under certain condition satisfied by the domain of geodesic parameter of all geodesics.

math.DG↗

arXiv2022

Sprays on Hamel-Funk Functions Model

Hamel functions of a spray play an important role in the study of the projective metrizability of the concerned spray, and Funk functions are special Hamel functions. A Finsler metric is a special Hamel function of the spray induced by the metric itself and a Funk metric is a special Funk function of a Minkowski spray. In this paper, we study sprays on a Hamel or Funk function model. Firstly, we give some basic properties of a Hamel or Funk function of a spray and some curvature properties of a Hamel or Funk function in projective relations. We use the Funk metric to construct a family of sprays and obtain some of their curvature properties and their metrizability conditions. Secondly, we consider the existence of Funk functions on certain spray manifold. We prove that there exist local Funk functions on a R-flat spray manifold, and on certain projectively flat Berwald spray manifolds, we construct a multitude of nonzero Funk functions. Finally, we introduce a new class of sprays called Hamel or Funk sprays associated to given sprays and Hamel or Funk functions. We obtain some special properties of a Hamel or Funk spray of scalar curvature, especially on its metrizability and a special form of its Riemann curvature.

math.DG↗

arXiv2022

On Sprays of Scalar Curvature and Metrizability

Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In this paper, a new notion, sprays of constant curvature, is introduced and especially it shows that a spray of isotropic curvature is not necessarily of constant curvature even in dimension $n\ge3$. Further, complete conditions are given for sprays of isotropic (resp. constant) curvature to be Finsler-metrizabile. As applications of such a result, the local structure is determined for locally projectively flat Berwald sprays of isotropic (resp. constant) curvature which are Finsler-metrizable, and some more sprays of isotropic curvature are discussed for their metrizability. Besides, the metrizability problem is also investigated for sprays of scalar curvature under certain curvature conditions.

math.DG↗

arXiv2021

On Concircular Transformations In Finsler Geometry

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a Finsler manifold. We characterize a concircular vector field with some PDEs on the tangent bundle, and then we obtain respective necessary and sufficient conditions for a concircular vector field to be conformal and a conformal vector field to be concircular. We also show conditions for two conformally related Finsler metrics to be concircular, and obtain some invariant curvature properties under conformal and concircular transformations.

math.DG↗

arXiv2018

A Note On Conformal Vector Fields Of $(α,β)$-Spaces

In this paper, we characterize conformal vector fields of any (regular or singular) $(α,β)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(α,β)$-spaces satisfying certain geometric conditions.

math.DG↗

arXiv2017

Conformal Vector Fields On Projectively Flat $(α,β)$-Finsler Spaces

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(α,β)$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fields are not necessarily homothetic.

math.DG↗

arXiv2017

On $m$-Kropina Finsler Metrics of Scalar Flag Curvature

In this paper, we consider a special class of singular Finsler metrics: $m$-Kropina metrics which are defined by a Riemannian metric and a $1$-form. We show that an $m$-Kropina metric ($m\ne -1$) of scalar flag curvature must be locally Minkowskian in dimension $n\ge 3$. We characterize by some PDEs a Kropina metric ($m=-1$) which is respectively of scalar flag curvature and locally projectively flat in dimension $n\ge 3$, and obtain some principles and approaches of constructing non-trivial examples of Kropina metrics of scalar flag curvature.

math.DG↗

arXiv2016

Conformal Vector Fields of a Class of Finsler Spaces II

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(α,β)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of $(α,β)$ spaces under certain curvature conditions. Besides, we construct a family of non-homothetic conformal vector fields on a family of locally projectively Randers spaces.

math.DG↗

arXiv2016

An accelerator scenario for hard X-ray free electron laser joint with high energy electron radiography

In order to study the dynamic response of the material and the physical mechanism of the fluid dynamics, an accelerator scenario which can be applied to hard X-ray free electron laser and high energy electron radiography was proposed. This accelerator is mainly composed of a 12GeV linac, an undulator branch and an eRad beamline. In order to characterize sample's dynamic behavior in situ and real-time with XFEL and eRad simultaneously, the linac should be capable of accelerating the two kinds of beam within the same operation mode. Combining with in-vacuum and tapering techniques, the undulator branch can produce more than 1E11 photons per pulse in 0.1 precent bandwidth at 42keV. Finally, the eRad amplifying beamline with 1:10 ratio was proposed as an important complementary tool for the wider view field and density identification ability.

physics.acc-ph↗

arXiv2015

On a Class of Complete and Projectively Flat Finsler Metrics

An $(α,β)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $α$ and $1$-form $β$ on the manifold $M$. In this paper, we classify $n$-dimensional $(α,β)$-manifolds (non-Randers type) which are positively complete and locally projectively flat. We show that the non-trivial class is that $M$ is homeomorphic to the $n$-sphere $S^n$ and $(S^n,F)$ is projectively related to a standard spherical Riemannian manifold, and then we obtain some special geometric properties on the geodesics and scalar flag curvature of $F$ on $S^n$, especially when $F$ is a metric of general square type.

math.DG↗

arXiv2014

A Note on a Class of Finsler Metrics of Isotropic S-Curvature

An $(α,β)$-metric is defined by a Riemannian metric and $1$-form. In this paper, we investigate the known characterization for $(α,β)$-metrics of isotropic S-curvature. We show that such a characterization should hold in dimension $n\ge 3$, and for the 2-dimensional case, there is one more class of isotropic S-curvature than the higher dimensional ones. Further, we construct corresponding examples for every two-dimensional class, especially for the class that the norm of $β$ with respect to $α$ is not a constant.

math.DG↗

arXiv2014

On a Class of Two-Dimensional Einstein Finsler Metrics of Vanishing S-Curvature

An $(α,β)$-metric is defined by a Riemannian metric $α$ and $1$-form $β$. In this paper, we study a known class of two-dimensional $(α,β)$-metrics of vanishing S-curvature. We determine the local structure of those metrics and show that those metrics are Einsteinian (equivalently, isotropic flag curvature) but generally are not Ricci-flat.

math.DG↗

arXiv2013

First experimental research of low energy proton radiography

Proton radiography is a new scatheless diagnostic tool, and which provides a potential development direction for advanced hydrotesting. Recently a low energy proton radiography system has been developed at CAEP. This system has been designed to use 11MeV proton beam to radiograph thin static objects. This system consists of a proton cyclotron coupled to an imaging beamline. The design features and commissioning results of this radiography system are presented.

physics.acc-ph↗

arXiv2013

On A Class of Finsler Metrics of Einstein-Reversibility

In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In particular, we show that all p-power metrics but Randers metrics, square metrics and 2-dimensional square-root metrics, are always Ricci-flat-parallel. Further, the local structure is almost determined for 2-dimensional square-root metrics which are Einsteinian (equivalently, of isotropic flag curvature), and examples show such metrics are not necessarily Ricci-flat.

math.DG↗

arXiv2013

On a Class of Two-Dimensional Singular Douglas and Projectively flat Finsler Metrics

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of two-dimensional singular Finsler metrics defined by a Riemann metric $α$ and 1-form $β$, and we characterize those which are Douglasian or locally projectively flat by some equations. It shows that the main class induced is an $m$-Kropina metric plus a linear part on $β$. For this class, the local structure of Douglasian or (in part) projectively flat case is determined, and in particular we show that a Kropina metric is always Douglasian and a Douglas $m$-Kropina metric with $m\ne -1$ is locally Minkowskian. It indicates that the two-dimensional case is quite different from the higher dimensional ones.

math.DG↗

arXiv2013

On a Class of Singular Douglas and Projectively flat Finsler Metrics

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of singular Finsler metrics defined by a Riemann metric $α$ and 1-form $β$ and characterize those which are respectively Douglasian and locally projectively flat in dimension $n\ge 3$ by some equations. Our study shows that the main class induced is an $m$-Kropina metric plus a linear part on $β$. For this class with $m\ne -1$, the local structure of projectively flat case is determined, and it is proved that a Douglas $m$-Kropina metric must be Berwaldian and a projectively flat $m$-Kropina metric must be locally Minkowskian. It indicates that the singular case is quite different from the regular one.

math.DG↗

arXiv2013

On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(α,β)$-metrics which are locally projectively flat with constant flag curvature in dimension $n= 2$ and $n \ge 3$ respectively. Further, we determine the local structure of $m$-Kropina metrics and particularly Kropina metrics which are projectively flat with constant flag curvature and prove that such metrics must be locally Minkowskian but are not necessarily flat-parallel.

math.DG↗

arXiv2013

On a Class of Finsler Metrics of Scalar Flag Curvature

We have shown that the Beltrami Theorem in Riemannian geometry is still true for square metrics if the dimension $n\ge 3$, namely, an $n(\ge 3)$-dimensional square metric is locally projectively flat if and only if it is of scalar flag curvature. In this paper, we go on with the study of the Beltrami Theorem for a larger class of $(α,β)$-metrics $F=αϕ(β/α)$ including square metrics, where $ϕ(s)$ is determined by a family of known ODEs satisfied by projectively flat $(α,β)$-metrics. For this class, we prove that the Beltrami Theorem holds if $β$ is closed, and in particular, we prove that $β$ must be closed for a subclass with $ϕ(s)$ being a polynomial of degree two. Further, we obtain the local and in part the global classifications to those metrics of scalar flag curvature.

math.DG↗