Locally conformal Kähler submersions
type: Item
instance of: scholarly article
title: Locally conformal Kähler submersions
zbMATH Open document ID: 0810.53054
DOI: 10.1007/BF01278477
author: J. Rocha
author: Juan Carlos Marrero
published in: Geometriae Dedicata
publication date: 1995-04-09T00:00:00Z
review text: Almost Hermitian submersions with total space a locally conformal Kähler manifold are called locally conformal Kähler submersions. The authors derive necessary and sufficient conditions for the fibers of such a submersion to be minimal and for the horizontal distribution to be completely integrable. As a consequence they point out that a result of \textit{E. Musso} [Boll. Unione Mat. Ital., VII. Ser., A 3, No. 2, 171-176 (1989; Zbl 0679.53055)] is not true in general. Moreover: (1) some relations between the Betti numbers of the total space and the base space are deduced, especially when the fibers are totally geodesic submanifolds; (2) the transfer of structures and some geometric properties on locally conformal Kähler submersions with total space a generalized Hopf manifold are studied; and (3) all the locally conformal Kähler submersions with totally geodesic fibers and total space a particular class of generalized Hopf manifolds are obtained.
reviewed by: Luis A. Cordero
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 679548
zbMATH Keywords: minimal fibre
zbMATH Keywords: almost Hermitian submersions
zbMATH Keywords: locally conformal Kähler submersions
zbMATH Keywords: Betti numbers
zbMATH Keywords: totally geodesic submanifolds
zbMATH Keywords: generalized Hopf manifold
zbMATH Keywords: totally geodesic fibers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 679548