A note on ``Sur le noyau de l'opérateur de courbure d'une variété Finslérienne'' (Q387786)

The authors consider \(\mathbb{R}^3\) endowed with a pseudo-Finsler function of Berwald-Moor type \(F:= e^{-x_1x_2}(y_1y_2y_3)^{1/3}\) and using a MAPLE program they compute the local coefficients of the Barthel connection and the components of the h-curvature tensor \(R\) of the Cartan connection. Then they provide the explicit forms for the kernel \(\mathcal{K}_R\) and the nullity distribution \(\mathcal{N}_R\) concluding that these do not coincide, in contradiction with an assertion made by \textit{H. Akbar-Zadeh} [C. R. Acad. Sci., Paris, Sér. A 272, 807--810 (1971; Zbl 0209.26001)]. Nevertheless, the authors find a sufficient condition for the coincidence and show that their condition holds in some nontrivial cases.