The generalized Cartan-Ambrose-Hicks theorem
The purpose of the present paper is to generalize the well-known Ambrose theorem and the Hicks theorem [\textit{N. Hicks}, Ill. J. Math. 3, 242-254 (1959; Zbl 0088.381), ibid. 10, 661-679 (1966; Zbl 0184.252)]. Though similar conditions are given which imply the local or global existence of connection-preserving mappings between manifolds endowed with Cartan connections, the new proof by the authors differs significantly from the original ones, since the authors construct the mapping between the frame bundles over the manifolds rather than between the manifolds themselves. Instead of broken geodesics considered in the Ambrose theorem, \(\omega\)- curves are considered where \(\omega\) is the 1-form of the Cartan connection and an \(\omega\)-curve is a curve generated by a vector field X such that \(\omega\) (X) is constant.
scientific article; zbMATH DE number 4103908