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• W2951119608 abstract "In this article we study the sub-Riemannian geometry of the spheres $S^{2n+1}$ and $S^{4n+3}$, arising from the principal $S^1-$bundle structure defined by the Hopf map and the principal $S^3-$bundle structure given by the quaternionic Hopf map respectively. The $S^1$ action leads to the classical contact geometry of $S^{2n+1}$, while the $S^3$ action gives another type of sub-Riemannian structure, with a distribution of corank 3. In both cases the metric is given as the restriction of the usual Riemannian metric on the respective horizontal distributions. For the contact $S^7$ case, we give an explicit form of the intrinsic sub-Laplacian and obtain a commutation relation between the sub-Riemannian heat operator and the heat operator in the vertical direction." @default.
• W2951119608 created "2019-06-27" @default.
• W2951119608 creator A5033739739 @default.
• W2951119608 creator A5063920482 @default.
• W2951119608 date "2010-08-31" @default.
• W2951119608 modified "2023-09-27" @default.
• W2951119608 title "Sub-Riemannian geodesics and heat operator on odd dimensional spheres" @default.
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