Holonomic spaces


The purpose of this note is to give a synthetic description of the intrinsic metric of a fiber F of the connection metric on a vector bundle E \rightarrow M over a riemannian manifold M endowed with a euclidean metric and a compatible connection. These metrics are described in terms of the action of the holonomy group and several properties are derived thereafter. In the process, a strong metric geometric meaning is given to the holonomy group.

DOI Code: 10.1285/i15900932v37suppl1p141

Keywords: Holonomy; vector bundles; connection metrics; isoholonomic; geodesics

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