Title:
Analysis on the unit sphere S^{3}
Abstract:
The unit sphere S^{3} can be identified with the unitary
group SU(2).
Under this identification the unit sphere can be considered as a
noncommutative Lie group.
The commutation relations for the vector fields of the corresponding Lie
algebra define
a 2step subRiemannian manifold.
In this talk, we present a geometrically meaningful formula for the
fundamental solutions to a second order subelliptic
differential equation and to the heat equation associated with
a subelliptic operator in the subRiemannian geometry
on the unit sphere S^{3}.
