2. Submanifolds in Engel manifolds

Problem 2.1.
Can properties of the space of closed Engel curves be used to distinguish Engel structures? In particular for the standard Engel structure on $\mathbb{R}^4$, is there a difference between homotopy of Engel loops and formal homotopy of Engel loops?
Remark. E. Murphy conjectures that nonrigid Engel knots obey an hprinciple.

Problem 2.2.
Is there an hprinciple for transverse embedded surfaces in a given Engel structure?
Remark. Already the following special case is interesting. Take a contact 3manifold and two transverse knots that are not transversely isotopic but have equal formal invariants. Are they transverse Engel concordant through a surface in a standard Engel structure on the product of the 3manifold with the interval?

Cite this as: AimPL: Engel structures, available at http://aimpl.org/engelstr.