Spherically symmetric Finsler metrics satisfying the $σ$T-condition

Abstract

In this paper, we present a complete characterization of spherically symmetric Finsler metrics that satisfy the $σT$-condition. We further investigate the subclass of such metrics within the Landsberg category and identify the precise conditions under which spherically symmetric Finsler metrics satisfying the $T$-condition must also be Berwaldian. In addition, we construct new non-regular solutions to the classical unicorn problem, providing explicit examples of Landsberg metrics that are not Berwaldian.