SIGMA 2 (2006), 067, 7 pages      math.DG/0609177      doi:10.3842/SIGMA.2006.067

The Relation Between the Associate Almost Complex Structure to HM¢ and (HM¢,S,T)-Cartan Connections

Ebrahim Esrafilian and Hamid Reza Salimi Moghaddam
Department of Pure Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Narmak-16, Tehran, Iran

Received April 08, 2006, in final form August 30, 2006; Published online September 06, 2006

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 Kähler manifold.

Key words: almost complex structure; Kähler and pseudo-Finsler manifolds; (HM¢,S,T)-Cartan connection.

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