Journal of Finsler Geometry and its Applications
https://jfga.uma.ac.ir/
Journal of Finsler Geometry and its Applicationsendaily1Wed, 01 May 2024 00:00:00 +0330Wed, 01 May 2024 00:00:00 +0330Analysis 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.Special projective algebra of exponential metrics of isotropic S-curvature
https://jfga.uma.ac.ir/article_2999.html
Exponential metrics are popular Finsler metrics. Let F be a exponential (&alpha;, &beta;)-metric of isotropic S-curvature on manifold M. In this paper, We study a Lie sub-algebra of projective vector fields of a Finsler metric F is introduced denoted by SP(F). We classify SP(F) of isotropic S-curvature as a certain Lie sub-algebra of the Kiliing algebra k(M, &alpha;).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 projectively flat Finsler space with n-power (α,β)-metric
https://jfga.uma.ac.ir/article_3000.html
In this paper we have taken the n-power (&alpha;,&beta;)-metric and obtained the condition for projectively flatness and further find the some special cases.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.Developing fixed point literature on the Branciari-Bakhtin-metric space
https://jfga.uma.ac.ir/article_3001.html
In the generalizing Branciari space, some conclusions from the literature are developed and re-proved in this paper.On projectively related Finsler gradient Ricci solitons
https://jfga.uma.ac.ir/article_3096.html
In this paper, we study pointwise projectively related Finsler gradient Ricci solitons. We obtain an equation that characterizes the relationship between two pointwise projectively related Finsler gradient Ricci solitons. Further, if two Finsler gradient Ricci solitons (M, F, dVF) and (M, F, dVF) satisfy &nbsp;some conditions,&nbsp; we characterize their relationships along the geodesics. In particular, if two Finsler gradient Ricci solitons are both complete, then (M, F, dVF) is expanding or shrinking and (M, F, dVF) is shrinking.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.On special weakly M - projective symmetric manifolds
https://jfga.uma.ac.ir/article_3097.html
The notion of a weakly symmetric and weakly projective symmetric Riemannian manifolds has been introduced by Tamassy and Binh and then after studied by so many authors such as De, Shaikh and Jana, Shaikh and Hui, Shaikh, Jana and Eyasmin. Recently, Singh and Khan introduced the notion of Special weakly symmetric Riemannian manifolds and denoted such manifold by (SWS)n. A.U. Khan and Q. Khan found some results On Special Weakly Projective Symmetric Manifolds. And P. Verma and S. Kishor found some results on M-Projective Curvature Tensor on (k, &micro;)- Contact Space Forms. Motivated from the above, we have studied the nature of Ricci tensor R of type (1,1) in a special weakly M-projective symmetric Riemannian manifold (SWMS)n and also explored some interesting results on (SWMS)n.On quintic (α,β)-metrics in Finsler geometry
https://jfga.uma.ac.ir/article_2870.html
&nbsp;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.Invariant square metrics on reduced Σ−spaces
https://jfga.uma.ac.ir/article_3098.html
In this paper, we study some geometric properties of Finsler &Sigma;&minus;spaces with square metric. We prove that Finsler &Sigma;&minus;spaces with square (&alpha;, &beta;)&minus;metrics are Riemannian.On the flag curvature of left invariant generalized m-Kropina metrics on some Lie groups
https://jfga.uma.ac.ir/article_3174.html
In this paper we study invariant Finsler spaces with generalized m-Kropia metrics. We give an explicit formula for the flag curvature of invariant Finsler spaces with generalized m-Kropina metrics on some Lie groups.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.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.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.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 metricsSome 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.Sacks-Uhlenbeck α−harmonic maps from Finsler manifolds
https://jfga.uma.ac.ir/article_3175.html
In this paper, we study the stability of Sacks-Uhlenbeck &alpha;&minus;harmonic maps from a Finsler manifold to a Riemannian manifold and its applications. Then we find conditions under which any non-constant &alpha;&minus;harmonic maps from a compact Finsler manifold to a standard unit sphere Sn(n &gt; 2) is unstable.