Geometric flow on compact locally conformally Kahler manifolds

Details Geometric flow on compact locally conformally Kahler manifolds Geometric flow on compact locally conformally Kahler manifolds

2001-05-05

arxiv.org/abs/math/0105040v2

Mathematics

Differential Geometry

Latex; New version of math.DG/0105040

Scientific paper

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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