C^1 Analysis of Hermite Subdivision Schemes on Manifolds

We propose two adaptations of linear Hermite subdivision schemes to operate on manifold-valued data. Our approach is based on a Log-exp analogue and on projection, respectively, and can be applied to both interpolatory and noninterpolatory Hermite schemes. 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 C^1-convergent linear scheme is also C^1 if certain technical conditions are met.