  Subdivision schemes have become an important tool for approximation of
manifold-valued functions. In this paper, we describe a construction of
manifold-valued subdivision schemes for geodesically complete manifolds. Our
construction is based upon the adaptation of linear subdivision schemes using
the notion of repeated binary averaging, where as a repeated binary average we
propose to use the geodesic inductive mean. We derive conditions on the adapted
schemes which guarantee convergence from any initial manifold-valued sequence.
The definition and analysis of convergence are intrinsic to the manifold. The
adaptation technique and the convergence analysis are demonstrated by several
important examples.
