Twisted basic Dolbeault cohomology on transverse Kähler foliations

Abstract

In this paper, we study the twisted basic Dolbeault cohomology and transverse hard Lefschetz theorem on a transverse Kahler foliation. And we give some properties for ${\Delta }_{\kappa }$-harmonic forms and prove the Kodaira-Serre type duality for the twisted basic Dolbeault cohomology.

18 pages. arXiv admin note: text overlap with arXiv:1709.05469