Canonical metric connections with constant holomorphic sectional curvature

Shuwen Chen; Fangyang Zheng

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arXiv · 2501.03032

Canonical metric connections with constant holomorphic sectional curvature

Shuwen Chen·Fangyang Zheng

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Abstract

We consider the conjecture of Chen and Nie concerning the space forms for canonical metric connections of compact Hermitian manifolds. We verify the conjecture for two special types of Hermitian manifolds: complex nilmanifolds with nilpotent $J$, and non-balanced Bismut torsion-parallel manifolds.

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Shuwen Chen, Fangyang Zheng. 2025-01-06. Canonical metric connections with constant holomorphic sectional curvature. https://arxiv.org/abs/2501.03032

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