The Relation Between the Associate Almost Complex Structure to $H{M}^{\prime }$ and $(H{M}^{\prime },S,T)$-Cartan Connections

Abstract

In the present paper, the $(H{M}^{\prime },S,T)$-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 $H{M}^{\prime }$. We prove that the natural almost complex linear connection associated to a $(H{M}^{\prime },S,T)$-Cartan connection is a metric linear connection with respect to the Sasaki metric $G$. Finally we give some conditions for $(M^{\prime },J,G)$ to be a Kähler manifold.

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