Final answer:
Sub-Riemannian geometry and contact geometry are both branches of mathematics that study different types of geometries. Sub-Riemannian geometry involves the constraints on the metric in a space, while contact geometry studies hypersurfaces called contact manifolds.
Step-by-step explanation:
Sub-Riemannian geometry studies the geometry of curves and surfaces in spaces where the metric is constrained by a set of vector fields. These vector fields define permissible directions of motion at each point, leading to a non-Euclidean geometry. Contact geometry, on the other hand, studies the geometry of hypersurfaces called contact manifolds, where each point is associated with a hyperplane called the contact plane. This geometry is used to study physical phenomena such as friction and adhesion.