Journal of Finsler Geometry and its Applications
https://jfga.uma.ac.ir/
Journal of Finsler Geometry and its Applicationsendaily1Fri, 01 Dec 2023 00:00:00 +0330Fri, 01 Dec 2023 00:00:00 +0330On a class of conformally flat (α,β)-metrics with special curvature properties
https://jfga.uma.ac.ir/article_2503.html
This paper is devoted to study of a class of conformally flat (&alpha;,&beta;)-metrics that have of the form F = &alpha;exp(2s)/s; where s := &beta;/&alpha;. They are called Kropina change of exponential (&alpha;,&beta;)-metrics. We prove that if F has relatively isotropic mean Landsberg curvature or almost vanishing Xi-curvature then it is a Riemannian metric or a locally Minkowski metric. Also, we prove that, if F be a weak Einstein metric, then it is either a Riemannian metric or a locally Minkowski metric.Analysis of generalized quasilinear hyperbolic and Boussinesq equations from the point of view of potential symmetry
https://jfga.uma.ac.ir/article_2866.html
Using the Lie classical method, the potential symmetry of the generalized hyperbolic quasilinear and Boussinesq equations is investigated. To find these symmetries in specific cases, we study various scientific examples that admit these symmetries. In addition, using this method, the potential symmetries of the conservative forms of the Boussinesq equation is determined.On six- dimensional Finsler space
https://jfga.uma.ac.ir/article_2867.html
The objective of this research paper is to comprehensively explore the main scalars within the cotext of the six- dimensional Finsler space. This investigation leverages both h-connection vectors and v- connection vectors. Additionally we have introduced the T-condition and v-curvature tensor S_hijk and express them in an extended form in relation to scalars and tensors in terms of main scalars.On the compatibility of supermetrics with nonlinear connections
https://jfga.uma.ac.ir/article_2504.html
One of the Helmholtz conditions for the inverse problem of a &lrm;Lagrangian Mechanics is the metric compatibility of a semispray&lrm; &lrm;and the associated nonlinear connection with a generalized&lrm; &lrm;Lagrange metric&lrm;. &lrm;In this paper&lrm;, &lrm;with respect to the supermetric&lrm; &lrm;induced by the Hessian of the Lagrangian&lrm;, &lrm;we find a family of&lrm; &lrm;nonlinear connections compatible with supermetric&lrm;. &lrm;In a particular case&lrm;, &lrm;when a Lagrangian superfunction&lrm; &lrm;is regular&lrm;, &lrm;we have a solution for the Euler-Lagrange&lrm;&lrm;superequation which&lrm; &lrm;defines a metric nonlinear connection&lrm;.An example of conformally Osserman manifold
https://jfga.uma.ac.ir/article_2868.html
In this paper, we investigate pseudo-Riemannian manifolds those eigenvalues of the Weyl conformal Jacobi operators are constant on the unit sphere bundles. Using a result of [4], we give an explicit construction of conformally Osserman manifold which is not locally conformally flat.On Kropina transformation of exponential (α,β)-metrics
https://jfga.uma.ac.ir/article_2869.html
In this paper&lrm;, &lrm;we study the Kropina transformation of exponential (&alpha;,&beta;)-metric F=&alpha;\exp(s),&nbsp; s:=&beta;/&alpha;&lrm;. &lrm;We characterize the conditions under which this class of (&alpha;,&beta;)-metric is locally projectively flat&lrm;, &lrm;locally dually flat&lrm;, &lrm;and Douglas metric&lrm;. &lrm;Based on&lrm;, &lrm;we show that the Kropina transformation of an exponential (&alpha;,&beta;)-metric is locally projectively flat&lrm;, &lrm;locally dually flat and Douglas metric if and only if the exponential (&alpha;,&beta;)-metric is locally projectively flat&lrm;, &lrm;locally dually flat and Douglas metric&lrm;, &lrm;respectively.The size of quasicontinuous maps on Khalimsky line
https://jfga.uma.ac.ir/article_2505.html
In the following text we show if D is Khalimsky line (resp. Khalimsky plane, Khalimsky circle, Khalimsky sphere), then for topological space X we show the collection of all quasicontinuous maps from D to X has cardinality card(X)&alefsym;.Projective Ricci curvature of Randers metrics of navigation data point of view
https://jfga.uma.ac.ir/article_2506.html
The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projective Ricci flat isotropic S-curvature Randers metrics from a navigation data point of view and conclude that these metrics are weak Einsteinian.Invariant Infinite series metrics on reduced Σ-spaces
https://jfga.uma.ac.ir/article_2507.html
In this paper we study the geometric properties of Finsler &Sigma;-spaces . we prove that Infinite series &Sigma;-spaces are Riemannian.On quintic (α,β)-metrics in Finsler geometry
https://jfga.uma.ac.ir/article_2870.html
Abstract. In this paper, we study the class of quintic (&alpha;,&beta;)-metrics. We show that every weakly Landsberg 5-th root (&alpha;,&beta;)-metrics has vanishing S-curvature. Using it, we prove that a quintic (&alpha;,&beta;)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. Then, we show that a quintic (&alpha;,&beta;)-metric satisfies &Xi; = 0 if and only if S = 0.An algorithm for constructing A-annihilated admissible monomials in the Dyer-Lashof algebra
https://jfga.uma.ac.ir/article_2508.html
We present an algorithm for computing A-annihilated elements of the form QI[1] in H*QS0 where I runs through admissible sequences of positive excess. This is algorithm with polynomial time complexity to address a sub-problem of an unsolved problem in algebraic topology known as the hit problem of Peterson which is likely to be NP-hard.On non-Riemannian quantities in Finsler geometry
https://jfga.uma.ac.ir/article_2701.html
This paper introduces new non-Riemannian quantities and classes of Finsler metrics. The study focuses on the class of Generalized Douglas Weyl GDW-metrics, which is contained in the class of Finsler metrics. The paper constructs the new sub-classes of GDW-metrics and presents illustrative examples.Some algebraic and topological structures of Fourier transformable functions
https://jfga.uma.ac.ir/article_2871.html
In this work, the set of all functions that are Fourier transformable with regard to their structure both algebraic and topological is taken into account. Certain topological properties of the set of Fourier transformable functions with the help of a metric are described. Also determines the proofs of the statements that the set of all Fourier transformable functions is a commutative semi-group with respect to the convolution operation as well as Abelian group with respect to the operation of addition. Metric for two functions belonging to the set of all Fourier transformable functions is defined and the proof that the Fourier transformable functions space is complete with our metric is given. The separability theorem and that the Fourier transformable functions space is disconnected are also discussed.On class of square Finsler metrics
https://jfga.uma.ac.ir/article_2702.html
In this paper, we remark some of the well-known curvature properties of square Finsler metrics. Then, we study weakly stretch square Finsler metrics.Generalized η-Ricci solitons on f -Kenmotsu manifolds admitting a quarter symmetric metric connection
https://jfga.uma.ac.ir/article_2878.html
In this paper, we study &eta;-Ricci solitons on 3-dimensional f-Kenmotsu manifolds with respect to a quarter symmetric metric connection. We obtain some results when the potential vector field is pointwise collinear with the Reeb vector field, conformal Killing vector field and a torqued vector field.Direction independence of the mean Landsberg tensor
https://jfga.uma.ac.ir/article_2879.html
Finsler manifolds some of whose characteristic tensors are direction independent provide stimulation for current research. In this paper, we show that the direction independence of the mean Landsberg tensor implies the vanishing of these tensor.Two classes of weakly Landsberg Finsler metrics
https://jfga.uma.ac.ir/article_2706.html
In this paper, we investigate the mean Landsberg curvature of two subclasses of (&alpha;,&beta;)-metrics. We prove that these subclasses of (&alpha;,&beta;)-metrics with vanishing mean Landsberg curvature have vanishing S-curvature. Using it, we prove that these Finsler metrics are weakly Landsbergian if and only if they are Berwaldian.Characteristics of T--conformal mappings
https://jfga.uma.ac.ir/article_2895.html
In this paper, we introduce the notion of T-conformal transformations and T-conformal maps between Riemannian manifolds. Here, T stands for a smooth (1,1)-tensor field defined on the domain of these maps. We start by defining what it means for a map to be T-conformal and also dwell on some basic properties of such type maps. We next specialize our discussion to the situation when the map T satisfies the condition &nabla;T = 0. Accordingly, we prove Liouville's theorem for T-conformal maps between space forms Rn(c) as an application under the condition &nabla;T = 0. The proof relies upon properties of T-conformal maps proved earlier. Broadly, the paper seeks to provide a general understanding of conformal mappings in the presence of a tensor field T and show how classical results such as Liouville's theorem apply.Geodesic vectors of infinite series (α, β)-metric on hypercomplex four dimensional Lie groups
https://jfga.uma.ac.ir/article_2731.html
In this paper, we consider invariant infinite series &nbsp;(&alpha;, &beta;)--metrics. Then we describe all geodesic vectors of this spaces on the left invariant hypercomplex four dimensional simply connected Lie groups.The necessary and sufficient condition for Cartan’s second curvature tensor which satisfies recurrnce and birecurrence property in generalized Finsler spaces
https://jfga.uma.ac.ir/article_2732.html
The recurrence and birecurrence property in Finsler space have been studied by the Finsleriangeometrics. The aim of this paper is to obtain the necessary and sufficient condition for Cartan&rsquo;s secondcurvature tensor that is recurrnt and birecurrent in generalized BP&minus;recurrent space and generalizedBP&minus;birecurrent space, respectively. We discuss certain identities belong to the mentioned spaces. Further,we end up this paper with some illustrative examples.On projective Riemann quadratic (PR-quadratic) Finsler metrics
https://jfga.uma.ac.ir/article_2896.html
This paper focuses on Projective Riemann quadratic (PR-quadratic) Finsler metrics, which are a variant of the Finsler metric in Finsler geometry. The paper introduces a special class of PR-quadratic Finsler metrics, called SPR-quadratic Finsler metrics, which is closed under projective changes with respect to a fixed volume form on M. This class contains the class of Douglas-Weyl metrics and is a subset of the class of Weyl metrics. The paper shows that any SPR-quadratic Finsler metric has a scalar flag curvature and a PR-quadratic Finsler metric has a scalar curvature if and only if it is of SPR-quadratic type. The results presented in this paper contribute to a deeper understanding of the behavior of PR-quadratic Finsler metrics and provide insights into the geometric properties of these metrics.On C3-like Finsler spaces of relatively isotropic mean Landsberg curvature
https://jfga.uma.ac.ir/article_2938.html
In this paper, we study the class of C3-like Finsler metrics with relatively isotropic mean Landsberg. We find some conditions under which these metrics reduce to relatively isotropic Landsberg metricsOn Riemannian and Ricci curvatures of Ingarden-Támassy metrics
https://jfga.uma.ac.ir/article_2733.html
In this paper, we study reversibility of Riemann Curvature and Ricci curvature for the Ingarden-T&aacute;massy metric and prove two global results. First, we prove that a Ingarden-T&aacute;massy metric is R-reversible if and only if si = 0, sij|k = 0. Then we show that a Ingarden-T&aacute;massy metric is Ricci-reversible if and only if si = 0.Some rigidity results on homogeneous Finsler spaces equipped with Killing frames
https://jfga.uma.ac.ir/article_2939.html
Utilizing Killing frames on homogeneous Finsler manifolds, we express the Berwald and mean Berwald curvatures in terms of Killing frames and get some rigidity results among them we prove that homogeneous isotropic weakly Berwald metrics reduce to weakly Berwald metric.