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The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Ebrahim Esrafilian; Hamid Reza Salimi Moghaddam. The Relation Between the Associate Almost Complex Structure to $HM'$ and $(HM',S,T)$-Cartan Connections. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a66/

[1] Bejancu A., Farran H. R., Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers, 2000 | MR

[2] Bejancu A., Farran H. R., “A comparison between the induced and the intrinsic Finsler connections on a Finsler submanifold”, Algebras Groups Geom., 16 (1999), 11–22 | MR | Zbl

[3] Brandt H. E., “Complex spacetime tangent bundle”, Found. Phys. Lett., 6 (1993), 245–255 | DOI | MR

[4] Brandt H. E., “Differential geometry of spacetime tangent bundle”, Internat. J. Theoret. Phys., 31 (1992), 575–580 | DOI | MR | Zbl

[5] Brandt H. E., “Finsler-spacetime tangent bundle”, Found. Phys. Lett., 5 (1992), 221–248 | DOI | MR

[6] Brandt H. E., “Kähler spacetime tangent bundle”, Found. Phys. Lett., 5 (1992), 315–336 | DOI | MR

[7] Crampin M., Kähler and para-Kähler structures associated with Finsler spaces of non-zero constant flag curvature, Preprint available from, 2005 ; here | MR

[8] Ichijyo Y., “Almost complex structures of tangent bundles and Finsler metrics”, J. Math. Kyoto Univ., 6 (1967), 419–457 | MR

[9] Ichijyo Y., “On the Finsler group and an almost symplectic structure on a tangent bundle”, J. Math. Kyoto Univ., 28 (1988), 153–163 | MR | Zbl

[10] Kobayashi S., Nomizu K., Foundations of differential geometry, V. 2, Interscience Publishers, John Wiley Sons, 1969 | MR | Zbl

[11] Matsumoto M., Foundations of Finsler geometry and special Finsler spaces, Kaiseisha, Japan, 1986 | MR | Zbl

[12] Wu B. Y., Some results on the geometry of tangent bundle of a Finsler manifold, Preprint, 2006