Nullity distributions associated with Chern connection

Abstract

The nullity distributions of the two curvature tensors R∗ and P∗ of the Chern connection of a Finsler manifold are investigated. The completeness of the nullity foliation associated with the nullity distribution NR∗ is proved. Two counterexamples are given: the first shows that NR∗ does not coincide with the kernel distribution of R∗; the second illustrates that NP∗ is not completely integrable. We give a simple class of a non-Berwaldian Landsberg spaces with singularities.