Morse-Novikov cohomology of locally conformally Kahler manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Ornea, Liviu^1,2  Verbitsky, Misha³ 

[1] Univ Bucharest, Fac Math, Bucharest 70109, Romania

[2] Simion Stoilow Romanian Acad, Inst Math, Bucharest 010702, Romania

[3] Inst Theoret & Expt Phys, Moscow 117259, Russia

关键词: Locally conformally Kahler;    Morse-Novikov cohomology;    Bott-Chern cohomology;    Vaisman manifold;    Weight bundle;   

DOI  :  10.1016/j.geomphys.2008.11.003

来源: Elsevier

【 摘 要 】

A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering, with the monodromy acting on this covering by holomorphic homotheties. We define three cohomology invariants, the Lee class, the Morse-Novikov class, and the Bott-Chern class, of an LCK-structure. These invariants play together the same role as the Kahler class in Kahler geometry. If these classes coincide for two LCK-structures, the difference between these Structures can be expressed by a smooth potential. similar to the Kahler case. We show that the Morse-Novikov class and the Bott-Chern class of a Vaisman manifold vanish. Moreover, for any LCK-structure oil a manifold, admitting a Vaisman structure, we prove that its Morse-Novikov class vanishes. We show that a compact LCK-manifold M with vanishing Bott-Chern class admits a holomorphic embedding into a Hopf manifold, if dim(C) M >= 3, a result which parallels the Kodaira embedding theorem. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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