Generalized transversely projective structure on a transversely holomorphic foliation (Q1608166)

Summary: The results of \textit{I. Biswas} [Conform. Geom. Dyn. 5, 74--80 (2001; Zbl 0977.37026)] 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 \({\mathbb C}{\mathbb P}^{n}\), 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 \(N^{ \otimes -k}\) for each \(k\in [ 3,n+1]\), where \(N\) is the normal bundle to the foliation. These transversely holomorphic sections are also flat with respect to the Bott partial connection.