[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c190084

REMARKS ON A THEOREM OF CUPIT-FOUTOU AND ZAFFRAN

Kim, Jin Hong (Department of Mathematics Education Chosun University)

Publication Information

Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 591-602 More about this Journal

Abstract

There is a well-known class of compact, complex, non-Kählerian manifolds constructed by Bosio, called the LVMB manifolds, which properly includes the Hopf manifold, the Calabi-Eckmann manifold, and the LVM manifolds. As in the case of LVM manifolds, these LVMB manifolds can admit a regular holomorphic foliation 𝓕. Moreover, later Meersseman showed that if an LVMB manifold is actually an LVM manifold, then the regular holomorphic foliation 𝓕 is actually transverse Kähler. The aim of this paper is to deal with a converse question and to give a simple and new proof of a well-known result of Cupit-Foutou and Zaffran. That is, we show that, when the holomorphic foliation 𝓕 on an LVMB manifold N is transverse Kähler with respect to a basic and transverse Kähler form and the leaf space N/𝓕 is an orbifold, N/𝓕 is projective, and thus N is actually an LVM manifold.

Keywords

LVM manifolds; LVMB manifolds; holomorphic foliations; transverse $K{\ddot{a}}hler$ ;

Citations & Related Records

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