In this paper we first study some global properties of the energy functional on a nonreversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the...

A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples metrics are Randers with closed [Formula: see text]-forms. Another family well-known projectively flat on text]-sphere that have constant positive curvature. In this paper, we prove some and dynamical characterizations metrics, several rigidity resul...

In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature, without the restriction of strong convexity (regularity). A classification result for the case ‖β‖α > 1 is provided, which is similar to the famous Bao-Robles-Shen’s result for strongly convex Randers metrics (‖β‖α < 1). Based on some famous vacuum Einstein metrics in General R...

Abstract We consider the cosmological evolution in an osculating point Barthel–Randers type geometry, which to each of space-time manifold arbitrary vector field is associated. This Finsler geometry assumed describe physical properties gravitational field, as well dynamics. For connection given by Levi-Civita associated Riemann metric. The generalized Friedmann equations are obtained considerin...

We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...

In this paper, we investigate the deflection of a charged particle moving in equatorial plane Kerr-Newman spacetime, focusing on weak field limit. To end, use Jacobi geometry, which can be described three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and ($n+1$)-dimensional stationary spacetime picture. Based Randers data Gauss-Bonnet theorem, utilize osculating R...

In this paper we study lifted left invariant $(\alpha,\beta)$-metrics of Douglas type on tangent Lie groups. Let $G$ be a group equipped with $(\alpha,\beta)$-metric $F$, induced by Riemannian metric $g$. Using vertical and complete lifts, construct the $F^v$ $F^c$ $TG$ give necessary sufficient conditions for them to type. Then, flag curvature these metrics are studied. Finally, as some specia...

Data Resource Profile: The Danish National Prescription Registry Anton Pottegård,* Sigrun Alba Johannesdottir Schmidt, Helle Wallach-Kildemoes, Henrik Toft Sørensen, Jesper Hallas and Morten Schmidt Clinical Pharmacology and Pharmacy, University of Southern Denmark, Odense, Denmark, Department of Clinical Epidemiology, Aarhus University Hospital, Aarhus, Denmark, Social and Clinical Pharmacy, U...