Modified action and differential operators on the 3-D sub-Riemannian sphere (Q2431508)
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scientific article
| Language | Label | Description | Also known as |
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| English | Modified action and differential operators on the 3-D sub-Riemannian sphere |
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Modified action and differential operators on the 3-D sub-Riemannian sphere (English)
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15 April 2011
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In this interesting paper, the authors deduce a geometrically meaningful formula for the Green function for a second order hypoelliptic differential operator and the heat kernel associated with this operator in the sub-Riemannian geometry on the unit sphere \(\mathbb{S}^3\). The method is based on the Hamiltonian-Jacobi approach, where the Hamiltonian system is solved with mixed boundary conditions. A closed form of the modified action is given. Also, the connection with optimal control is presented.
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sub-Riemannian geometry
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action
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sub-Laplacian
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heat kernel
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geodesic
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Hamiltonian system
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optimal control
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