A graphic study of wave front sets of exponential sub-Riemannian maps is performed for homogeneous three dimensional sub-Riemannian manifolds. We verify that depending on dimension of the sub-Riemannian isometry group of the manifold, the first singularities of wave front sets are of two types. If the group is four dimensional, the singularity is a conjugate point. If the group is three dimensional, there are two conjugate points and the wave front set intersects along a segment which connects both points.
@article{1519,
title = {Wave Front Sets Singularities of Homogeneous Sub-Riemannian Three Dimensional Manifolds},
journal = {CUBO, A Mathematical Journal},
volume = {10},
year = {2008},
language = {en},
url = {http://dml.mathdoc.fr/item/1519}
}
Ayala, V´ıctor; Diniz, Marcos M.; Lima, Jos´e C.P.; Veloso, Jos´e M.M.; Tribuzy, Ivan. Wave Front Sets Singularities of Homogeneous Sub-Riemannian Three Dimensional Manifolds. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1519/