Nullity distributions associated with Chern connection

Nabil L. Youssef, S. G. Elgendi

Published 2014-10-01Version 1

The Klein-Grifone approach to global Finsler geometry is adopted. The nullity distributions of the two curvature tensors \, $\overast{R}$ and $\overast{P}$ of Chern connection are investigated. The completeness of the nullity foliation associated with the nullity distribution $\N_{R^\ast}$ is proved. Two counterexamples are given. The fitst shows that $\N_{R^\ast}$ dose not coincide with the kernel distribution of \, $\overast{R}$. The second shows that $\N_{P^\ast}$ is not completely integrable and, as a by-product, it provides an example of a Landesbergian non Berwaldian space.