  A classical result in Riemannian geometry states that the absolutely
continuous curves into a (finite-dimensional) Riemannian manifold form an
infinite-dimensional manifold. In the present paper this construction and
related results are generalised to absolutely continuous curves with values in
a strong Riemannian manifolds. As an application we consider extensions of the
square root velocity transform (SRVT) framework for shape analysis.
Computations in this framework frequently lead to curves which leave the shape
space (of smooth curves), and are only contained in a completion. In the vector
valued case, this extends the SRVT to a space of absolutely continuous curves.
We investigate the situation for shape spaces of manifold valued (absolutely
continuous) curves.
