Modified Action and Differential Operators on the 3-D Sub-Riemannian Sphere
Chang, Der-Chen ; Markina, Irina ; Vasil'ev, Alexander
Asian J. Math., Tome 14 (2010) no. 1, p. 439-474 / Harvested from Project Euclid
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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 $S^3$. Our method is based on the Hamiltonian-Jacobi 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 $S^3$.
Publié le : 2010-12-15
Classification:  Sub-Riemannian geometry,  action,  sub-Laplacian,  heat kernel,  geodesic,  Hamiltonian system,  optimal control,  53C17,  70H05 
@article{1298989627,
     author = {Chang, Der-Chen and Markina, Irina and Vasil'ev, Alexander},
     title = {Modified Action and Differential Operators on the 3-D Sub-Riemannian Sphere},
     journal = {Asian J. Math.},
     volume = {14},
     number = {1},
     year = {2010},
     pages = { 439-474},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1298989627}
}

Chang, Der-Chen; Markina, Irina; Vasil'ev, Alexander. Modified Action and Differential Operators on the 3-D Sub-Riemannian Sphere. Asian J. Math., Tome 14 (2010) no. 1, pp.  439-474. http://gdmltest.u-ga.fr/item/1298989627/