The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections

Details The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections

2006-09-06

arxiv.org/abs/math/0609177v1

SIGMA 2 (2006), 067, 7 pages

Mathematics

Differential Geometry

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.067

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 K\"ahler manifold.

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