"Theory of singularities of smooth mappings and around it". November 25～29, 2013. edited by Takashi Nishimura. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.A subriemannian manifold (M, D, g) is a differential manifold M equipped with a subbundle D of the tangent bundle TM of M. We emphasize abnormal extremals (abnormal geodesics) in subriemannian geometry and in particular show results of abnormal extremals on Cartan distributions of growth (2, 3, 5). The subriemannian geometry is very important in differential geometry and it is closely related to the control theory
