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arXiv · 0809.2735

Modified action and differential operators on the 3-D sub-Riemannian sphere

Der-Chen Chang·Irina Markina·Alexander Vasil'ev
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Abstract

Our main aim is to present a geometrically meaningful formula for the fundamental solutions to a second order sub-elliptic differential equation and to the heat equation associated with a sub-elliptic operator in the sub-Riemannian geometry on the unit sphere $\mathbb S^3$. Our method is based on the Hamiltonian approach, where the corresponding Hamitonian system is solved with mixed boundary conditions. A closed form of the modified action is given. It is a sub-Riemannian invariant and plays the role of a distance on $\mathbb S^3$.

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Der-Chen Chang, Irina Markina, Alexander Vasil'ev. 2008-09-16. Modified action and differential operators on the 3-D sub-Riemannian sphere. https://arxiv.org/abs/0809.2735

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