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

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dc.creatorChang, Der-Chen
dc.creatorMarkina, Irina
dc.creatorVasil'ev, Alexander
dc.date2008-09-16
dc.date.accessioned2026-07-07T10:03:17Z
dc.date.available2026-07-07T10:03:17Z
dc.descriptionOur 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 $\mathbb S^3$.
dc.description35 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0809.2735
dc.identifierhttp://arxiv.org/abs/0809.2735
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169232
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C17, 70H05
dc.titleModified action and differential operators on the 3-D sub-Riemannian sphere
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