JOURNAL OF FINSLER GEOMETRY AND ITS APPLICATIONS
Year:2025 | Volume:6 | Issue:1|Papers Count:12

In this paper we study the complex Lagrange space with a special (γ,β)-metric and determined the fundamental metric tensor, its inverse Euler-Lagrange equation, complex semi-spray coefficient, complex non-linear connection as well as Chern-Lagrange connections for Lagrange space with the mentioned special metric.

The aim of the present paper is to study the Lagrange spaces due to changed (α,β)-metric with Z. Shen square- Randers metric L ̅= 〖(α+β)〗^2/α+ β and obtained fundamental tensor fields for these space. Further, we studied about the variational problem with fixed endpoints for the Lagrange spaces due to above change.

The article discusses the application of tension field and harmonic maps in image processing. It introduces the concept of (α,f)- harmonic maps, which encompasses both α- harmonic maps and f-harmonic maps, and delves into their characteristics. Furthermore, it presents a Liouville type theorem for this kind of harmonic maps

In this paper, we study about the rst eigenvalue of the bi-Laplace operator on Finsler manifolds. Considering a bounded weighted Ricci curvature on a complete Finsler manifold, we obtain an upper bound for the first eigenvalues of Buckling and Clamped plate problems related with the first eigenvalue of the laplace operator.

In this paper, we study Ricci semi-symmetric null hypersurfaces in a Lorentzian space form. We give a necessary and sufficient condition for a screen quas-conformal null hypersurface to be Ricci semi-symmetric. We show that every screen quasi-conformal null hypersurface M of R1m+2 such that rank *Aξ < m is Ricci semi-symmetric. Next, we give a local classification of a Ricc semi-symmetric screen conformal null hypersurface of a Lorentzian space form.

Deformation of every spray into a projective spray can be done using a volume form on a manifold. The Riemann curvature of a projective spray is called the projective Riemmann curvature. In this paper, we present a global rigidity result for projectively PR-flat sprays that have vanishing Douglas curvature. Then we study and characterize projectively PR-flat Randers metrics of Douglas curvature‎.

In the following text for Khalimsky n-dimensional space Kn we show self-map f:Kn →Kn has closed graph if and only if there exist integers λ1,...,λn such that f is a constant map with value (2λ1,...,2λn). We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples.

In this paper, we give a parametrization of the set of algebraic points of degree at most l over Q on the hyperelliptic curve y2 = x(x2 + x - 4)(x2 - x + 45) This curve was studied by Bruin and Flynn in [4] where the heights explicitly described the set of rational points, i.e. C(1)(Q). Drawing on the work of Arnth-Jensen and Flynn based on [2] and one of Abel-Jacobi's fundamental theorems in [1, 8], we extend the results of [4] to algebraic points of any degree which we denote C(l)(Q).

In this paper, we introduce a contact pseudo-metric structure on a tangent sphere bundle TεM. we prove that the tangent sphere bundle TεM is (κ, μ)-contact pseudo-metric manifold if and only if the manifold M is of constant sectional curvature. Also, we prove that this structure on the tangent sphere bundle is K-contact iff the base manifold has constant curvature ε.

The present paper considers duals‎, ‎approximate duals and pseudo-duals of generalized frames in Hilbert C*-modules‎. ‎In particular‎, ‎the ones constructed by bounded operators inserted between the synthesis and analysis operators of a Bessel sequence are focused and characterized‎. ‎Moreover‎, ‎the mentioned notions for modular g-Riesz bases are studied and some of their properties are obtained.

In this paper, we introduce a novel class of graphs based on Hilbert spaces, termed Hilbert graphs. Constructed using the inner product defined on a Hilbert space, Hilbert graphs leverage the concept of orthogonality, where orthogonal elements correspond to adjacent vertices. We demonstrate that Hilbert graphs are regular and vertex transitive, with the clique number equal to the dimension of the corresponding Hilbert space. Our investigation encompasses various properties of Hilbert graphs, including connectivity, girth, diameter, and chromatic number, and we draw comparisons with Cayley graphs and zero divisor graphs.

The purpose of the present paper is to discuss about a generalized Sasakian space form with quarter-symmetric metric connection satisfying h-almost conformal Ricci-Bourguignon soliton and h-almost conformal η-Ricci-Bourguignon soliton. Here, we have evolved the nature of h-almost conformal Ricci-Bourguignon soliton on a generalized Sasakian space form with quarter-symmetric metric connection when the potential vector field is to be considered as a conformal vector field, a torse-forming vector field or a torqued vector field. Then we have established that a generalized Sasakian space form with quarter-symmetric metric connection satisfying gradient h-conformal Ricci-Bourguignon soliton to turn out an Einstein manifold. Later, we have constructed Laplacian equation from h-almost conformal η-Ricci-Bourguignon soliton with quarter-symmetric metric connection when the potential vector field ξ is of gradient of a smooth function f. Finally we have examined the existence of an extended generalized φ-recurrent generalized Sasakian space form with quarter-symmetric metric connection endowing h-almost conformal η-Ricci-Bourguignon soliton.