Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection
Year: 2026
Type: preprint
Abstract: Noguchi introduced the notion of Wronskian curvature positivity in his Second Main Theorem and asked for further examples to which his theorem applies. We give a complete answer: a complex manifold admits a smooth connection satisfying this condition if and only if it admits a holomorphic projective connection. For a fixed torsion-free connection, the condition is equivalent to the holomorphicity of its projective class.
Source: arXiv (Cornell University)
Authors: Wang, Pengchao, Xie, Songyan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1603846912, G7519385794, G8533620077
OpenAlex ID: W7168234571