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Calabi-Yau Hyperbolicity

  • Abdelouahab Khelifati
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Abstract

The goal of this paper is to introduce a new notion of hyperbolicity for compact complex manifolds with trivial canonical bundle, called \textit{Calabi--Yau hyperbolicity}. We investigate its fundamental properties and establish a characterization in terms of the fundamental group. In particular, we show that no compact Kähler Calabi--Yau manifold is Calabi--Yau hyperbolic, highlighting the genuinely non-Kähler nature of this notion. We also investigate different techniques for constructing examples of such manifolds. Finally, we examine the relationship between Calabi--Yau hyperbolicity and Kobayashi hyperbolicity in the examples considered, highlighting obstructions to the latter in the Calabi--Yau setting.

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Cite

BibTeXRIS
BibTeX
@misc{khelifati2026calabiyau,
  title = {{Calabi-Yau Hyperbolicity}},
  author = {Abdelouahab Khelifati},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37996},
  eprint = {2610.37996},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37996},
}
RIS
TY  - UNPB
TI  - Calabi-Yau Hyperbolicity
AU  - Abdelouahab Khelifati
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37996
UR  - https://arxiv.org/abs/2610.37996
AB  - The goal of this paper is to introduce a new notion of hyperbolicity for compact complex manifolds with trivial canonical bundle, called \textit{Calabi--Yau hyperbolicity}. We investigate its fundamental properties and establish a characterization in terms of the fundamental group. In particular, we show that no compact Kähler Calabi--Yau manifold is Calabi--Yau hyperbolic, highlighting the genuinely non-Kähler nature of this notion. We also investigate different techniques for constructing examples of such manifolds. Finally, we examine the relationship between Calabi--Yau hyperbolicity and Kobayashi hyperbolicity in the examples considered, highlighting obstructions to the latter in the Calabi--Yau setting.
ER  -