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PreprintarXiv licencearXiv

Non-Kähler Hyperbolicity: Surfaces and Codimension One

  • Samir Marouani
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Abstract

We study hyperbolicity notions for compact complex manifolds defined by special Hermitian metrics and by holomorphic maps from ℂn−1 (divisorial hyperbolicity). For surfaces we show that divisorial and Brody hyperbolicity coincide and that Hermitian-symplectic and Kähler hyperbolicity coincide when h2,0=0. In any dimension we prove obstructions to Gauduchon hyperbolicity, show that projective spaces are not divisorially hyperbolic, and give divisorially hyperbolic manifolds that are not balanced hyperbolic.

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Cite

BibTeXRIS
BibTeX
@misc{marouani2026nonkähler,
  title = {{Non-Kähler Hyperbolicity: Surfaces and Codimension One}},
  author = {Samir Marouani},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07098},
  eprint = {2611.07098},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07098},
}
RIS
TY  - UNPB
TI  - Non-Kähler Hyperbolicity: Surfaces and Codimension One
AU  - Samir Marouani
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07098
UR  - https://arxiv.org/abs/2611.07098
AB  - We study hyperbolicity notions for compact complex manifolds defined by special Hermitian metrics and by holomorphic maps from ℂ^n−1 (divisorial hyperbolicity). For surfaces we show that divisorial and Brody hyperbolicity coincide and that Hermitian-symplectic and Kähler hyperbolicity coincide when h^2,0=0. In any dimension we prove obstructions to Gauduchon hyperbolicity, show that projective spaces are not divisorially hyperbolic, and give divisorially hyperbolic manifolds that are not balanced hyperbolic.
ER  -