the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

Abstract In this work, we extend the study of Schwarzschi ld–Finsler–Randers (SFR) spacetime previously investigated by a subset present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis 81(11):990, 2021). We will examine dynamical analysis geodesics which provides derivation energy and angular momentum particle moving along geodesic SFR spacetime. This allows us ...

Abstract Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence metric provides way encode Lorentz-violating effects into geometric structure spacetime. Here, classical field theory proposed in special geometry, so-called Randers-Finsler spacetime, where violation produced by background vector field. By promoting dif...

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 1. Introduction. The geometry of Finsler manifolds of constant flag curvature is one of the fundamental subjects in Finsler geometry. Akbar-Zadeh [1] proved that, u...