细察Calabi-Eguchi-Hanson空间
微分几何
2025-08-25 v2
摘要
本文细察Eguchi-Hanson与Calabi在复射影空间典范线丛上引入的Ricci平坦度量。我们将这些空间描述为某些轨道奇点的解消。随后显式计算曲率，并证明所有紧致极小子流形均包含于零截面中。这推广了Tsai与Wang的一个结果。
引用
@article{arxiv.2201.07295,
title = {A detailed look at the Calabi-Eguchi-Hanson spaces},
author = {Jørgen Olsen Lye},
journal= {arXiv preprint arXiv:2201.07295},
year = {2025}
}
备注
22 pages. The second version includes the following changes: Added a short result about the holomorphic volume form (Prop. 8), amended an important gap in the proof of Thm. 9, added a description of local coordinates on the canonical line bundle and described the metric in these coordinates (Eq. 22)