Dolbeault Cohomology Along the Vertical Liouville Distribution on Complex Finsler Bundles

Abstract

In this paper we define a vertical Liouville distribution in the vertical foliated distribution on a complex Finsler bundle and we prove that it is an integrable one. Next, some new operators on foliated forms along the vertical Liouville distribution are defined, a Dolbeault type lemma is proved and new cohomology groups are studied.