The relation between the associate almost complex structure to HM′ and (HM′, S,T)-cartan connections

Abstract

In the present paper, the (HM′, S, T)-Cartan connections on pseudo-Finsler manifolds, introduced by A. Bejancu and H.R. Farran, are obtained by the natural almost complex structure arising from the nonlinear connection HM′. We prove that the natural almost complex linear connection associated to a (HM′, S, T)-Cartan connection is a metric linear connection with respect to the Sasaki metric G. Finally we give some conditions for (M′, J,G) to be a Ka¨hler manifold.