Nullity distributions associated with Chern connection

Abstract

The nullity distributions of the two curvature tensors \, $\overast{R}$ and $\overast{P}$ of the Chern connection of a Finsler manifold are investigated. The completeness of the nullity foliation associated with the nullity distribution ${\mathbb{N}}_{R^{\ast }}$ is proved. Two counterexamples are given: the first shows that ${\mathbb{N}}_{R^{\ast }}$ does not coincide with the kernel distribution of \, $\overast{R}$; the second illustrates that ${\mathbb{N}}_{P^{\ast }}$ is not completely integrable. We give a simple class of a non-Berwaldian Landsberg spaces with singularities.

Major modifications, An Example added at the end of the paper, Some Maple calculations inserted