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arXiv · 1802.10292

Cahen-Gutt moment map, closed Fedosov star product and structure of the automorphism group

Akito Futaki·Hajime Ono
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Abstract

We show that if a compact Kaehler manifold $M$ of non-negative Ricci curvature admits closed Fedosov star product then the reduced Lie algebra of holomorphic vector fields on $M$ is reductive. This comes in pair with the obstruction previously found by La Fuente-Gravy. More generally we consider the squared norm of Cahen-Gutt moment map as in the same spirit of Calabi functional for the scalar curvature in cscK problem, and prove a Cahen-Gutt version of Calabi's theorem on the structure of the Lie algebra of holomorphic vector fields for extremal Kaehler manifolds. The proof uses a Hessian formula for the squared norm of Cahen-Gutt moment map.

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Akito Futaki, Hajime Ono. 2018-02-28. Cahen-Gutt moment map, closed Fedosov star product and structure of the automorphism group. https://arxiv.org/abs/1802.10292

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