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arXiv · 2407.12183

Rigidity of the subelliptic heat kernel on $\operatorname{SU}(2)$

Maria Gordina·Jing Wang
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Abstract

We study heat kernel rigidity for the Lie group $\operatorname{SU}\left( 2 \right)$ kernel equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to the Hopf fibration $\operatorname{U}\left( 1 \right)\to \operatorname{SU}\left( 2 \right)\to \mathbb{CP}^1$, which coincides with the sub-Riemannian sphere $\operatorname{SU}\left( 2 \right)$.

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Maria Gordina, Jing Wang. 2024-07-16. Rigidity of the subelliptic heat kernel on $\operatorname{SU}(2)$. https://arxiv.org/abs/2407.12183

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