On the geometry of randers manifolds

Abstract

Abstract. Randers manifolds are studied in the framework of the pullback bundle formalism, with the aid of intrinsic methods only. After checking a sufficient condition for a Randers manifold to be a Finsler manifold, we provide a systematic description of the Riemann-Finsler metric, the canonical spray, the Barthel endomorphism, the Berwald connection, the Cartan tensors and the Cartan vector field in this new setting. Finally, as an application of the new tools and geometric ideas developed here, we present an intrinsic proof of the celebrated theorem about a criterion for a Randers manifold to become a Berwald manifold.

A Finsler geodesic spray paradigm for wildfire spread modelling

“…We refer to [48,49,50,47,51,4,52,53,54,8,55,56,57,5,58,59,60] for details on Randers spaces and on the Zermelo navigation problem.…”

On the projective theory of sprays with applications to Finsler geometry

“…Using this, we obtain the following result, which can also be found in [41]. Lemma 6.1 The Cartan vector field of a Finsler manifold is g-orthogonal to the canonical section, i.e., g( * C, δ) = 0.…”

Energy <i>β</i>-Conformal Change and Special Finsler Spaces

“…However, this is not a connection on M but is a connection on T (TM), the tangent bundle of TM, or on π −1 (TM), the pullback of the tangent bundle TM by :TM M   . The infinitesimal transformations (changes) in Riemannian and Finsler geometry are important, not only in differential geometry, but also in application to other branches of science, especially in the process of geometrization of physical theories [1].…”