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2005 Geometric flow on compact locally conformally Kähler manifolds
Yoshinobu Kamishima, Liviu Ornea
Tohoku Math. J. (2) 57(2): 201-221 (2005). DOI: 10.2748/tmj/1119888335


We study two kinds of transformation groups of a compact locally conformally Kähler (l.c.K.) manifold. First, we study compact l.c.K. manifolds by means of the existence of holomorphic l.c.K. flow (i.e., a conformal, holomorphic flow with respect to the Hermitian metric.) We characterize the structure of the compact l.c.K. manifolds with parallel Lee form. Next, we introduce the Lee-Cauchy-Riemann ($\mathrm{LCR}$) transformations as a class of diffeomorphisms preserving the specific $G$-structure of l.c.K. manifolds. We show that compact l.c.K. manifolds with parallel Lee form admitting a non-compact holomorphic flow of $\mathrm{LCR}$ transformations are rigid: such a manifold is holomorphically isometric to a Hopf manifold with parallel Lee form.


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Yoshinobu Kamishima. Liviu Ornea. "Geometric flow on compact locally conformally Kähler manifolds." Tohoku Math. J. (2) 57 (2) 201 - 221, 2005.


Published: 2005
First available in Project Euclid: 27 June 2005

zbMATH: 1083.53068
MathSciNet: MR2137466
Digital Object Identifier: 10.2748/tmj/1119888335

Primary: 57S25
Secondary: 53C55

Rights: Copyright © 2005 Tohoku University


Vol.57 • No. 2 • 2005
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