C1 Analysis of Hermite Subdivision Schemes on Manifolds

We propose two adaptations of linear Hermite subdivisions schemes to operate on manifold-valued data based on a Log-exp approach and on projection, respectively. Furthermore, we introduce a new proximity condition, which bounds the difference between a linear Hermite subdivision scheme and its manifold-valued analogue. Verification of this condition gives the main result: The manifold-valued Hermite subdivision scheme constructed from a C1convergent linear scheme is also C1, if certain technical conditions are met.