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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 1999, Volume 6, Number 3/4, Pages 288–316
(Mi jmag416)
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Conforlmal submersions of Kählerian manifolds. II
S. I. Okrut Kharkiv State University
Abstract:
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.
Received: 25.05.1997
Citation:
S. I. Okrut, “Conforlmal submersions of Kählerian manifolds. II”, Mat. Fiz. Anal. Geom., 6:3/4 (1999), 288–316
Linking options:
https://www.mathnet.ru/eng/jmag416 https://www.mathnet.ru/eng/jmag/v6/i3/p288
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