Some Properties of Balanced Hyperbolic Compact Complex Manifolds
Complex Variables
2022-02-15 v2 Algebraic Geometry
Differential Geometry
Abstract
We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the harmonic spaces on the universal cover of these manifolds. Other results include a Hard Lefschetz-type theorem for certain compact complex balanced manifolds and the non-existence of certain currents on the universal covering space of a balanced hyperbolic manifold.
Cite
@article{arxiv.2107.09522,
title = {Some Properties of Balanced Hyperbolic Compact Complex Manifolds},
author = {Samir Marouani and Dan Popovici},
journal= {arXiv preprint arXiv:2107.09522},
year = {2022}
}
Comments
34 pages, to appear in International Journal of Mathematics