Journal of the
Korean Mathematical Society JKMS

We study the relation between an $R$-Cartan structure $\alpha$ and an $(I,J,K)$-generalized Finsler structure $\omega$ on a 3-manifold $\Sigma$ showing the difficulty in finding a general transformation that maps $\alpha$ to $\omega$. In some particular cases, the mapping can be uniquely determined by geometrical conditions. Moreover, we are led in this way to a negative answer to our conjecture in [12].

Keywords: generalized Finsler structures, foliations, exterior differential systems, surface of revolution

MSC numbers: Primary 53C60; Secondary 53C20, 58A15