Transformations of compact locally conformally Kähler manifolds

Yoshinobu Kamishima; Liviu Ornea

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Transformations of compact locally conformally Kähler manifolds

Yoshinobu Kamishima·Liviu Ornea

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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 $\mathbb{C}^*$.

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BibTeX RIS

Yoshinobu Kamishima, Liviu Ornea. 2000-11-08. Transformations of compact locally conformally Kähler manifolds. https://arxiv.org/abs/math/0011050

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