八元数 Hopf 纤维化上的次椭圆热核
微分几何
2020-01-15 v2 偏微分方程分析
摘要
我们研究 维单位球面上的次拉普拉斯算符，该算符通过相对于 Hopf 纤维化提升八元数射影空间的拉普拉斯算符得到。我们特别地获得了其热核的显式公式，并推导出相关次拉普拉斯算符的格林函数表达式。作为副产品，我们还得到了次拉普拉斯算符的谱、热核的小时间渐近，并显式计算了次黎曼距离。
引用
@article{arxiv.1904.08568,
title = {The subelliptic heat kernel of the octonionic Hopf fibration},
author = {Fabrice Baudoin and Gunhee Cho},
journal= {arXiv preprint arXiv:1904.08568},
year = {2020}
}
备注
Companion paper of arXiv:1112.3084 and of arXiv:1310.5938. The geometry is quite different but there is a natural overlap in the method of computing the heat kernel and its asymptotics once the formula for the radial part of the sub-Laplacian is obtained. v2 typos corrected and presentation improved