https://jfga.uma.ac.ir/ Journal of Finsler Geometry and its Applications en daily 1 Fri, 01 May 2026 00:00:00 +0330 Fri, 01 May 2026 00:00:00 +0330 https://jfga.uma.ac.ir/article_4154.html This paper develops a framework for defining intrinsic volumes on manifolds M by leveraging the structure of Weil bundles MA associated with Weil algebras A. We explore constructions for a Finsler-like structure FA primarily on the fibers of MA, aiming to derive it from the algebraic properties of A with minimal reliance on auxiliary metrics on M. The concept of A-naturality is introduced to formalize the intrinsic nature of such structures. From this fiberwise FA, an effective Finsler structure FM on the tangent bundle TM is derived. The Busemann-Hausdorff measure dVF associated with FM then provides a volume form on M. We establish foundational results concerning conditions under which a diffeomorphism ø: M → M preserves dVF, linking this to the behavior of its prolongation øA and exploring resulting rigidity phenomena, including a characterization theorem for dVF under affine symmetries. Furthermore, we propose several significant conjectures and future research directions concerning infinitesimal symmetries, axiomatic uniqueness of these volumes, interactions with curvature, sub-Riemannian limits, and holonomy restrictions. https://jfga.uma.ac.ir/article_4539.html Given any Finsler metric F on a smooth manifold, its symmetrized metric Fˆ(x,y):=1/2(F(x,y)+F(x,-y) may inherit some geometric properties of F. We examine this fact for the Matsumoto metric F=α2/(α-β) and prove that if the Matsumoto metric is locally projectively flat then, so is its symmetrized metric Fˆ=α3/(α2-β2). In particular, the converse result also holds. https://jfga.uma.ac.ir/article_4540.html In this paper, we define and construct the ruled surfaces in a three-dimensional strict Walker manifold. We study the geometric properties of these families of surfaces. We give an example to illustrate our main results. https://jfga.uma.ac.ir/article_4155.html This work investigates α-cosymplectic and N(k)-contact metric (CM) manifolds equipped with an HRS. We derive some characterization properties for these manifolds. https://jfga.uma.ac.ir/article_4541.html In this paper we introduce and study the classes of lower-C2 and upper-C2 functions on Hadamard manifolds. As applications, we investigate their regularity properties and analyze stationary points of associated minimization problems. Our results show that the class of lower-C2 functions is regular in this setting, while the class of upper-C2 functions is not. https://jfga.uma.ac.ir/article_4156.html In this paper, we study the characteristics of n-dimensional Lorentzian para-Kenmotsu manifolds (briefly, (LP K)n) endowed with the W7-curvature tensor. First,we analyzed (LP K)n manifolds under the condition W7(X, Y, Z, ξ) = 0. Next,we explore (LP K)n manifolds satisfying the W7-semisymmetric condition, ϕ-W7-symmetric condition, and ϕ-W7-flat condition. Moreover, we discuss Lorentzianpara-Kenmotsu manifolds under the condition W7(U, V ) · R = 0, and prove thatsuch manifolds reduce to Einstein manifolds. Finally, all the relevant results havebeen verified through an example. https://jfga.uma.ac.ir/article_4542.html The present study initially identifies the generalized symmetric connection of the type (α1, α2), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The goal of this endeavor is to look at the η-Ricci Soliton(RS) on Lorentzian metric P-Sasakian(PS) manifold with Generalized Symmetric Metric(GSM) connection of the kind (α1,α2). Ricci and η-Ricci solitons with generalized symmetric metric connection of the type (α1,α2) have been discussed, satisfying the curvature conditions Finally, we have constructed an example of LP-Sasakian manifold with generalized symmetric metric connection of the type (α1, α2) admitting η-Ricci solitons. https://jfga.uma.ac.ir/article_4157.html In this paper, we consider a shape optimization problem associated with the fractional Laplacian We focus on J( Omega) = j( Omega,u ) where u is the solution of 1.3. We give an existence ofoptimal shape using differents methods. These results are based compactness and cone property. We establish also the shape derivative and topological derivative of the functionalusing the minmax method. https://jfga.uma.ac.ir/article_4543.html In this paper, we investigate the geometry of contact pseudo-metric manifolds admitting an η-Ricci soliton. We establish that a Sasakian pseudo-metric manifold admitting an η-Ricci soliton is necessarily an η-Einstein manifold. Furthermore, if the potential vector field of the soliton is not Killing, then the manifold is D-homothetically fixed, and the vector field preserves the structure tensor field.We also prove that a K-contact pseudo-metric manifold endowed with a gradient η-Ricci soliton metric is η-Einstein. In addition, we examine contact pseudo-metric manifolds admitting an η-Ricci soliton whose potential vector field is pointwise colinear with the Reeb vector field. Finally, we analyze gradient η-Ricci solitons on (κ, μ)-contact pseudo-metric manifolds, providing new insights into their structure and curvature properties. https://jfga.uma.ac.ir/article_4234.html In this research paper, we have considered the various type of β-change in Finsler metric F such as square change Finsler metric, cubic change Finsler metric, quartic change Finsler metric and obtained fundamental metric tensor, Cartan's tensor of these metrics. Further, we obtained the necessary and sufficient conditions under which said metrics are projectively flat and also given a example to support our results. https://jfga.uma.ac.ir/article_4655.html In this paper, we introduce a new family of metrics on topological dynamical systems, induced by probability bi-sequences, which generalizes both the classical Bowen metric and the mean metric. Using these metrics, we define measure-theoretic and topological pressure and show that these quantities coincide with the classical topological pressure and the sum of measure-theoretic entropy and integral of the potential function, respectively. The results hold under the following mild condition on the probability bi-sequence Γ ={γm,n}m,n≥ 0:limsupn→∞ [(γn*)-1/n] < ∞,where γn* := min0≤ i ≤ nγi,n. This condition is satisfied for a broad class of bi-sequences, including the uniform weights γm,n = 1/(n+1) that recover the mean metric case. As an application, we extend the pressure versions of Katok's entropy formula to this more general setting. Our work unifies and generalizes several previous results on pressure in mean metrics. https://jfga.uma.ac.ir/article_4235.html In 1994, S. Basco and M. Matsumoto studied the concept of projective change between two Finsler spaces with (α,β)-metrics. Projective change between two Finsler metrics arises from Information Geometry. In the present paper, we find conditions to characterize the projective change between two (α,β)-metrics, such as special cubic (α,β)-metric and Randers metric on a manifold with dim n≥3, where α and   α-  are two Riemannian metrics, β and β-  are two non-zero 1-forms. https://jfga.uma.ac.ir/article_4656.html In this paper, we study Killing and 2-Killing vector fields on Vaidya spacetimes. We determine all Killing symmetries of the metric and obtain several classes of 2-Killing vector fields under the assumption of a single non-zero component. https://jfga.uma.ac.ir/article_4236.html ‎In this study‎, ‎we define the local components of the adapted connection relative to the adapted frame field‎. ‎We also calculate the covariant derivative of a tensor with respect to this connection‎. ‎Furthermore‎, ‎we present a classification of totally geodesic foliations and bundle-like metrics‎, ‎along with the introduction of the local components of the torsion tensor associated with this connection‎. ‎To illustrate our findings‎, ‎we provide a relevant example‎. https://jfga.uma.ac.ir/article_4237.html In this paper, we present a coordinate-free investigation of the generalized silver Finsler metric. Specifically, for a Finsler manifold (M, L)$and a 1-form B, we study various geometric structures associated with the Finsler metric L∼= L ∅(s), where ∅(s):= s2 - 2s - 1.The function ∅(s) has roots s1 = 1 - √2 and s2 = 1 +√2, where the positive root represents the so-called the silver ratio. Assuming that L is a Finsler metric, we refer to L∼ as the generalized silver Finsler metric. We derive the associated metric and Cartan tensors, along with other fundamental geometric objects. The non-degeneracy condition of the metric tensor of L∼ is characterized. We compute the geodesic spray, Barthel connection, and Berwald connection of L∼, when the 1-form B arises from a concurrent π-vector field. Furthermore, we determine the curvature of the Barthel connection associated with L∼. An illustrative example is also provided. https://jfga.uma.ac.ir/article_4238.html This paper investigates the properties and topological implications of gradient shrinking general Ricci flow (GRF) system solitons. A GRF system soliton is a solution that evolves through a one-parameter family of diffeomorphisms or scaling transformations. Under specific geometric constraints, such as bounded Ricci curvature or positive injectivity radius, we establish a lower bound for the potential function associated with these solitons. Furthermore, we demonstrate that any complete gradient shrinking GRF system soliton exhibits finite topological type. These results extend the understanding of geometric flows, linking them to broader applications in differential geometry and topology. https://jfga.uma.ac.ir/article_4295.html We introduce a new class of Finsler manifolds modelled on LP-Sasakian structures and develop their geometric properties. The paper defines Finsler LP-Sasakian manifolds, studies their curvature behavior, and formulates generalized η-Ricci solitons in this context. An explicit example is  provided, and several directions for future research are proposed. https://jfga.uma.ac.ir/article_4296.html In this paper, we study Lorentzian para-Kenmotsu manifolds endowed with a semi-symmetric metric connection and establish necessary and sufficient conditions under which the Ricci tensor is ω-parallel with respect to this connection. These results extend classical notions of Ricci parallelism from Riemannian geometry to a broader non-Riemannian framework. In addition, we examine the behavior of concircular and projective curvature tensors on such manifolds and derive structural identities that highlight the influence of semi-symmetric torsion on fundamental geometric invariants. To support our theoretical developments, we construct an explicit 4-dimensional illustration. The findings deepen the understanding of non-Riemannian geometric structures and suggest potential applications in generalized theories of gravity. https://jfga.uma.ac.ir/article_4297.html In this paper, we examine certain geometric properties of the curvature tensor for a special case of the Walker metric, assuming g33 = g44 = k̸ = 0, where k is a constant, on a 4-dimensional manifold. Finally, we investigate the necessary and sufficient conditions for the 4-dimensional manifold with this special case of the Walker metric to be locally symmetric.