Geometric analysis on the 3-D sphere

Der-Chen Chang (Georgetown)

Abstract: The unit sphere S3 can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding Lie algebra define a 2-step sub-Riemannian manifold. We study sub-Riemannian geodesics on this sub-Riemannian manifold making use of the Hamiltonian formalism. We also discuss some properties of the heat kernel for the sub-Laplacian.