Kähler Ricci孤子与复结构的形变
微分几何
2012-06-11 v2
摘要
给定一个紧致Fano Kähler流形(M,J)，其上有一个Kähler Ricci孤子g，我们考虑(M,J)的复形变族{J_t}，这些形变在(M,g)的全等距群中最大环面T的作用下不变。我们证明，在g的拉普拉斯算子谱的某个条件下，在每个与J足够接近的复流形(M, J_t)上，存在一个光滑的T不变Kähler Ricci孤子族g_t。该结果推广了Koiso关于Kähler Einstein流形复形变的定理。
引用
@article{arxiv.1206.0471,
title = {K\"ahler Ricci solitons and deformation of complex structures},
author = {Fabio Podesta' and Andrea Spiro},
journal= {arXiv preprint arXiv:1206.0471},
year = {2012}
}
备注
This preprint has been withdrawn by the authors. It stated a result which has been independently proved in a stronger version by H. Li in "Complex deformation of critical Kaehler metrics" posted in ArXiv:1206.0912 [math.DG]