Holomorphic Engel Structures

TL;DR

This paper introduces holomorphic Engel structures, explores their fundamental properties, provides examples, and characterizes them through positivity conditions, aiming to classify projective manifolds admitting such structures.

Contribution

It develops the theory of holomorphic Engel structures, presents new examples, and offers a classification framework based on positivity conditions.

Findings

Two series of examples of holomorphic Engel structures

Characterization of these structures via positivity conditions

Foundational properties established for the classification of manifolds

Abstract

Recently there has been renewed interest among differential geometers in the theory of Engel structures. We introduce holomorphic analogues of these structures, and pose the problem of classifying projective manifolds admitting them. Besides providing the basic properties of these varieties, we present two series of examples and characterize them by certain positivity conditions on the Engel structure.