On the Cartan torsion of Minkowskian product of Finsler manifolds

Abstract

In this paper, we investigate the Cartan torsion and mean Cartan torsion of the Minkowskian product of two Finsler metrics. We derive explicit formulas for both torsions and analyze their geometric behavior. In particular, we demonstrate that both the Cartan torsion and mean Cartan torsion decompose additively if and only if the Minkowskian product is Euclidean. Additionally, we provide a necessary and sufficient condition for the norm of the mean Cartan torsion to remain bounded in the Euclidean case.