Conforlmal submersions of K\"ahlerian manifolds.~II

S. I. Okrut

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 288-316.

Résumé

The paper is a continuation of the first part of work and concerns the research of global properties of Kählerian manifolds which admit a holomorphic conformal submersion with a vertical exponent of the conformality of the submersion onto some other Kählerian manifold; the submersion fibers are assumed to be geodesic. The Kählerian manifolds may be considered as a kählerian analogue of the crossed product in the Kählerian manifolds with the above submersion are necessarily fiber spaces with isomorphic fibers. A method is proposed of constructing bundles including complete and compact fibers of a non-Riemannian projection wich is a submersion of the same type. It is shown that for such bundles with one-dimensional fibers to exist, it is necessary and sufficient that the base be a Hodge manigold. It is given the holomorphic classification of possible all of complete one-dimensional fibers of submersion of the stated above type.