Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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