Transformations of compact locally conformally Kähler manifolds

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dc.creatorKamishima, Yoshinobu
dc.creatorOrnea, Liviu
dc.date2000-11-08
dc.date.accessioned2026-07-07T04:38:30Z
dc.date.available2026-07-07T04:38:30Z
dc.descriptionWe characterize compact locally conformally Kähler (l.c.K.) manifolds under the assumption of a purely conformal, holomorphic circle action. As an application, we determine the structure of the compact l.c.K. manifolds with parallel Lee form. We introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms preserving the specific $G$-structure of l.c.K. manifolds. Then we characterize the Hopf manifolds, up to holomorphic isometry, as compact l.c.K. manifolds admitting a certain closed LCR action of $\mathbb{C}^*$.
dc.description22 pages. Latex, uses amscd, amsmath, amssymb, amsfonts packages
dc.identifierhttps://arxiv.org/abs/math/0011050
dc.identifierhttp://arxiv.org/abs/math/0011050
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60302
dc.subjectDifferential Geometry
dc.titleTransformations of compact locally conformally Kähler manifolds
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