Geometric flow on compact locally conformally Kahler manifolds

2001/05/05 by Yoshinobu Kamishima, Y. Kamishima, Kamishima, Y. +3 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0105040

Latex; New version of math.DG/0105040

openalex publication_date 2001/05/05 · arxiv created 2002/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Calabi-Yau locally conformally Kähler manifolds
• Hermitian geometrically formal manifolds

Related

• Transformations of compact locally conformally Kähler manifolds
• Blow-ups of locally conformally Kahler manifolds
• Stable Bundles on Irregular Vaisman Manifolds
• Calabi-Yau locally conformally Kähler manifolds
• Kähler-Ricci flow and conformal submersion