A characterization of holonomy invariant functions on tangent bundles

作者：Aradi Bernadett^*; David Csaba Kertesz

来源：Balkan Journal of Geometry and Its Applications, 2014, 19(2): 1-10.

• holonomy invariance
• parallel translation
• parallelism
• generalized Berwald manifold
• one-form manifold

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a natural way. Thus, in particular, we obtain a characterization of generalized Berwald manifolds. We also construct a simple example of a generalized Berwald manifold which is not Berwald.

• 出版日期2014