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The Subelliptic Heat Kernel of the Octonionic Hopf Fibration
Potential Analysis ( IF 1.1 ) Pub Date : 2020-07-14 , DOI: 10.1007/s11118-020-09854-4
Fabrice Baudoin , Gunhee Cho

We study the sub-Laplacian of the 15-dimensional unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the octonionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of a related sub-Laplacian. As a byproduct we also obtain the spectrum of the sub-Laplacian, the small-time asymptotics of the heat kernel and explicitly compute the sub-Riemannian distance.



中文翻译:

辛酸Hopf纤维的亚椭圆热核。

我们研究了15维单位球的次拉普拉斯算子,它是通过相对于Hopf纤维提升张量的射影投影空间的拉普拉斯算子而获得的。我们特别获得了其热核的显式公式,并推导了相关的次拉普拉斯算子的格林函数的表达式。作为副产品,我们还获得了次拉普拉斯光谱,热核的小时间渐近性,并显式计算了次黎曼距离。

更新日期:2020-07-14
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