Generalized transversely projective structure on a transversely holomorphic foliation

Abstract

The results of Biswas (2000) are extended to the situation of transversely projective foliations. In particular, it is shown that a transversely holomorphic foliation defined using everywhere locally nondegenerate maps to a projective space ℂℙn, and whose transition functions are given by automorphisms of the projective space, has a canonical transversely projective structure. Such a foliation is also associated with a transversely holomorphic section of N⊗−k for each k∈[3,n+1], where N is the normal bundle to the foliation. These transversely holomorphic sections are also flat with respect to the Bott partial connection.