Related papers: Generalized Finsler structures on closed 3-manifol…
We study the relation between an R-Cartan structure {\alpha} and an (I, J, K)- generalized Finsler structure on a 3-manifold showing the difficulty in finding a general transformation that maps these structures each other. In some…
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian…
The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to $(M,L)$ and the corresponding…
Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…
On a smooth manifold M, generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on M. Given a complex manifold (M,j), we define six families of…
This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler manifolds. By leveraging Riemannian and Finsler geometry, we…
We study contact 3-manifolds $Y$ with a special global frame inspired by Cartan's structure equations. This frame is dual to a generalized Finsler structure defined by Bryant. We present some examples and rigidity results on the class of…
We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact…
The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning ({\alpha}, \beta})-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this…
The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed…
Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…
On a Finsler manifold $(M,L)$, we consider the change $L\longrightarrow\bar{L}(x,y)=e^{\sigma(x)}L(x,y)+\beta (x,y)$, which we call a $\beta$-conformal change. This change generalizes various types of changes in Finsler geometry: conformal,…
In this paper we adopt the pullback approach to global Finsler geometry. We investigate horizontally recurrent Finsler connections. We prove that for each scalar ($\pi$)1-form $A$, there exists a unique horizontally recurrent Finsler…
By a Randers' structure on a manifold $M$ we mean a Finsler structure $L^*=L+\alpha$, where $L$ is a Riemannian structure and $\alpha$ is a 1-form on $M$. This structure was first introduced by Randers ~\cite{[8]} from the standpoint of…
We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized K\"ahler manifold to be a generalized CRFK structure. Then, we discuss a notion of generalized almost contact structure…
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…
Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated. Such connection unifies all formerly known Finsler connections and some other connections not introduced so far. Also, our…
In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…
Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…