Related papers: Some fundamental problems in global Finsler geomet…
We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…
A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his…
The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the…
In this paper we introduce the concept of singular Finsler foliation, which generalizes the concepts of Finsler actions, Finsler submersions and (regular) Finsler foliations. We show that if $\mathcal{F}$ is a singular Finsler foliation on…
We define the notion of sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory. We compute a complete set of local invariants, geodesic equations, and the Jacobi operator for…
The objective of the present paper (the second in a series of four) is to give a theory of multivector and extensor fields on a smooth manifold M of arbitrary topology based on the powerful geometric algebra of multivectors and extensors.…
Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection ('pull-back formalism'), first we enrich the known lists of the characterizations of affine…
The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The…
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…
We provide observations that Finsler geometry could be useful tools to construct higher-spin theories. We suggest that a Finsler metric of constant flag curvature can be regarded as a metric encoding higher-spin fields. We also show that…
In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic…
This paper provides a comprehensive overview of the current state of research on Douglas curvature in Finsler spaces. It explores the significance, properties, and applications of Douglas curvature, and its role in understanding Finsler…
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter…
In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index Lemma that we will allow us to extend some classical results of finite…
Relying on the general theory of Lie derivatives a new geometric definition of Lie derivative for general spinor fields is given, more general than Kosmann's one. It is shown that for particular infinitesimal lifts, i.e. for Kosmann vector…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Ra\~{n}ada field. We consider the most general actions that are invariant under the Lorentz, electromagnetic…
The sub-Finslerian geometry means that the metric $F$ is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian…
Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the…
In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries and to metrics on Teichm{\"u}ller spaces. For a general…