Kähler and para-Kähler structures associated with Finsler spaces of non-zero constant flag curvature

• Autores: Mike Crampin
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 1, 2008, págs. 99-114
• Idioma: inglés
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• Resumen

  • It was shown by R.,L. Bryant (Houston J. Math. 28 (2002) 221-262) that there is a canonical Kähler structure on the space of geodesics of a Finsler manifold whose flag curvature is constant and positive. A different construction is proposed in the present paper, leading instead to a Kähler structure on the slit tangent bundle of the Finsler space; it is based on the identification of an appropriate complex structure. The construction is easily adapted to apply to a Finsler space with constant negative flag curvature, when it gives a para-Kähler rather than a Kähler structure; the properties of this para-Kähler structure are explored.