Quasi-Kähler manifolds with trivial Chern Holonomy

Antonio J. Di Scala; Luigi Vezzoni

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arXiv · 0807.1664

Quasi-Kähler manifolds with trivial Chern Holonomy

Antonio J. Di Scala·Luigi Vezzoni

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Abstract

In this paper we study almost complex manifolds admitting a quasi-Kähler Chern-flat metric (Chern-flat means that the holonomy of the Chern connection is trivial). We prove that in the compact case such manifolds are all nilmanifolds. Some partial classification results are established and we prove that a quasi-Kähler Chern-flat structure can be tamed by a symplectic form if and only if the ambient space is isomorphic to a flat torus.

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BibTeX RIS

Antonio J. Di Scala, Luigi Vezzoni. 2008-07-10. Quasi-Kähler manifolds with trivial Chern Holonomy. https://arxiv.org/abs/0807.1664

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