超凯勒流形上的抛物四元数Calabi-Yau方程
微分几何
2023-07-17 v3
摘要
我们证明紧致超凯勒流形上的抛物四元数Monge-Ampère方程总存在长时间解，该解经规范化后光滑收敛于四元数Monge-Ampère方程的解。这与Dinew和Sroka证明Alesker与Verbitsky猜想的设定相同。我们还引入了超厄米流形中Chern-Ricci流的类似物。
引用
@article{arxiv.2303.02689,
title = {The parabolic quaternionic Calabi-Yau equation on hyperk\"ahler manifolds},
author = {Lucio Bedulli and Giovanni Gentili and Luigi Vezzoni},
journal= {arXiv preprint arXiv:2303.02689},
year = {2023}
}
备注
This is a new version of the paper "The Calabi-Yau theorem on Hypercomplex manifolds", which was withdrawn due to a crucial mistake in a key Lemma. In this new version we fix the mistake by introducing the extra assumption of the existence of a background hyperk\"ahler metric