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Geometric flow on compact locally conformally Kahler manifolds

Y. Kamishima·L. Ornea
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Abstract

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms preserving the specific G-structure of l.c.K. manifolds. We show that compact l.c.K. manifolds admitting a non-compact CC^* flow of LCR transformations are rigid: it is holomorphically conformal to a Hopf manifold with parallel Lee form.

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Y. Kamishima, L. Ornea. 2002-07-17. Geometric flow on compact locally conformally Kahler manifolds. https://arxiv.org/abs/math/0105040

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