Abstract
Using a model for the bundle Fˆ2M of semi-holonomic second order frames of a manifold M as an extension of the bundle F2M of holonomic second order frames of M, we introduce in Fˆ2M a principal bundle structure over F2M, the structure group being the additive group A2(n) of skew-symmetric bilinear maps from Rn×Rn into Rn. The composition of the projection of that structure with the existing projection of the bundle F˜2M of non-holonomic second order frames of M over Fˆ2M provides a principal bundle structure in F˜2M over F2M. These results close an existing gap in the theory of second order frame bundles.
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