Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection

Pengchao Wang; Songyan Xie

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arXiv · 2607.11021

Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection

Pengchao Wang·Songyan Xie

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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.

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BibTeX RIS

Pengchao Wang, Songyan Xie. 2026-07-13. Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection. https://arxiv.org/abs/2607.11021

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