Journal of Finsler Geometry and its Applications
Volume:5 Issue: 1, May 2024

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.

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.

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.

In this paper‎, ‎we study the Kropina transformation of exponential (α,β)-metric F=α\exp(s),  s:=β/α‎. ‎We characterize the conditions under which this class of (α,β)-metric is locally projectively flat‎, ‎locally dually flat‎, ‎and Douglas metric‎. ‎Based on‎, ‎we show that the Kropina transformation of an exponential (α,β)-metric is locally projectively flat‎, ‎locally dually flat and Douglas metric if and only if the exponential (α,β)-metric is locally projectively flat‎, ‎locally dually flat and Douglas metric‎, ‎respectively.

Abstract. In this paper, we study the class of quintic (α,β)-metrics. We show that every weakly Landsberg 5-th root (α,β)-metrics has vanishing S-curvature. Using it, we prove that a quintic (α,β)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. Then, we show that a quintic (α,β)-metric satisfies Ξ = 0 if and only if S = 0.

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.

In this paper, we study η-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.

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.

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 ∇T = 0. Accordingly, we prove Liouville's theorem for T-conformal maps between space forms Rn(c) as an application under the condition ∇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.

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.

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 metrics

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.