English

Properties of Holomorphic $p$-Contact Manifolds

Differential Geometry 2025-11-17 v1 Algebraic Geometry Complex Variables

Abstract

We continue the study of compact holomorphic pp-contact manifolds XX that we introduced recently by expanding the discussion to include non-K\"ahler hyperbolicity issues and a differential calculus based on what we call the Lie derivative with respect to a (0,q)(0,\,q)-form with values in the holomorphic tangent bundle of XX. We also propose the notion of pp-contact deformations for which we prove a Bogomolov-Tian-Todorov-type unobstructedness theorem to order two. This kind of small deformations of the complex structure is related to the essential horizontal deformations that we introduced in our previous work and forms part of a wider on-going project aimed at developing a non-K\"ahler mirror symmetry theory that was first tested on the Iwasawa manifold and subsequently on Calabi-Yau page-11-ˉ\partial\bar\partial-manifolds.

Keywords

Cite

@article{arxiv.2511.10818,
  title  = {Properties of Holomorphic $p$-Contact Manifolds},
  author = {Hisashi Kasuya and Dan Popovici and Luis Ugarte},
  journal= {arXiv preprint arXiv:2511.10818},
  year   = {2025}
}

Comments

37 pages. This is essentially the second part, with slight additions, of our submission arXiv:2502.01447v1 that has been split into two. The original submission arXiv:2502.01447v1 will be updated, replaced with its first part and will become arXiv:2502.01447v2, referred to in the present submission as [KPU25]