Transformations of compact locally conformally Kähler manifolds

2000/11/08 by Yoshinobu Kamishima, Kamishima, Yoshinobu, Liviu Ornea +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/0011050

22 pages. Latex, uses amscd, amsmath, amssymb, amsfonts packages

arxiv created 2000/11/08 · arxiv updated 2009/11/30

Abstract

We 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 ℂ^*.

Related

• Geometric flow on compact locally conformally Kahler manifolds
• Calabi-Yau locally conformally Kähler manifolds
• Vaisman theorem for lcK spaces
• A note on locally conformally Kaehler structures and small deformations of Hopf manifolds
• A characterisation of toric LCK manifolds