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arXiv · 2608.23778

A characterization of complex projective space via the Calabi curvature operator

Hasan M. El-Hasan·Xiaolong Li·Jan Nienhaus·Peter Petersen·James Stanfield·Matthias Wink
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Abstract

We prove a Tachibana-type result for K\"ahler-Einstein manifolds isolating complex projective space based on its Calabi curvature operator. The proof uses a new Bochner formula expressing the Lichnerowicz curvature term via the Calabi curvature operator. This resolves one of the problems posed at the AIM workshop "The Bochner Technique'' (May 2026).

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Hasan M. El-Hasan, Xiaolong Li, Jan Nienhaus, Peter Petersen, James Stanfield, Matthias Wink. 2026-08-24. A characterization of complex projective space via the Calabi curvature operator. https://arxiv.org/abs/2608.23778

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