Geometric flow on compact locally conformally Kahler manifolds
Differential Geometry
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0105040,
title = {Geometric flow on compact locally conformally Kahler manifolds},
author = {Y. Kamishima and L. Ornea},
journal= {arXiv preprint arXiv:math/0105040},
year = {2007}
}
Comments
Latex; New version of math.DG/0105040