
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, Narmak16, 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 pseudoFinsler 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 pseudoFinsler manifolds; (HM',S,T)Cartan connection.
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