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arXiv · 2009.01741

Characterization of Curvature positivity of Riemannian metrics on flat vector bundles

Fusheng Deng·Xujun Zhang
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Abstract

We give a characterization of Nakano positivity of Riemannian flat vector bundles over bounded domains $D\subset\mathbb{R}^n$ in terms of solvability of the $d$ equation with certain good $L^2$ estimate condition. As an application, we give an alternative proof of the matrix-valued Prekopa's theorem that is originally proved by Raufi. Our methods are inspired by the recent works of Deng-Ning-Wang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles and positivity of direct image sheaves associated to holomorphic fibrations.

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Fusheng Deng, Xujun Zhang. 2020-09-01. Characterization of Curvature positivity of Riemannian metrics on flat vector bundles. https://arxiv.org/abs/2009.01741

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