Ebrahim Esrafilian, Hamid Reza Salimi Moghaddam, “The Relation Between the Associate Almost Complex Structure to <nobr>$HM'$</nobr> and <nobr>$(HM',S,T)$</nobr>-Cartan Connections”, SIGMA, 2006, Volume 2,067, 7 pp.

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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

Department of Pure Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Narmak-16, Tehran, Iran

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.

Keywords: almost complex structure; Kähler and pseudo-Finsler manifolds; $(HM',S,T)$-Cartan connection.

MSC: 53C07; 53C15; 53C60; 58B20

Received: April 8, 2006; in final form August 30, 2006; Published online September 6, 2006

Language: English

DOI: 10.3842/SIGMA.2006.067