Kaehlerian Finsler Manifolds

In the present paper, continued the preceding paper [10], we are mainly concerned with a Kaehlerian Finsler manifold (M, f, g). First, in the Kaehlerian Finsler manifold, we define a generalized Finsler metric g^^～ by g^^～=(g+^tfgf)/2. We investigate the relation between the Finsler metric g, the generalized Finsler metric g^^～, the complex structure f and several Finsler connections derived from g and g^^～. In consequence of it, we obtain that the Kaehlerian Finsler manifold is a Landsberg space and the generalized Finsler metric g^^～ can be regarded as a real representation of a complex Finsler metric in a sense. Finally we find a necessary and sufficient condition for an Hermitian structure on the tangent bundle over a Kaehlerian Finsler manifold to be a Kaehler structure.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。