Geometric flow on compact locally conformally Kahler manifolds

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概要

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• 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 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.

• 東北大学の論文

著者

• KAMISHIMA Yoshinobu

  Department of Mathematics Faculty of Science Hokkaido University

• Kamishima Yoshinobu

  Department Of Mathematics Tokyo Metropolitan University

• Ornea Liviu

  Faculty of Mathematics, University of Bucharest

• Ornea Liviu

  Faculty Of Mathematics University Of Bucharest

関連論文

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• On the 3-Dimensional Pseudo-Hermitian Space Forms and Other Geometric Structures
• Geometric flow on compact locally conformally Kahler manifolds
• Transformation groups on Heisenberg geometry

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