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

Ebrahim Esrafilian·Hamid Reza Salimi Moghaddam
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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.

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Ebrahim Esrafilian, Hamid Reza Salimi Moghaddam. 2006-09-06. The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections. https://doi.org/10.3842/sigma.2006.067

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