HORIZONTAL SUBSPACES IN THE BUNDLE OF LINEAR FRAMES Park, Joon-Sik;
Let L(M) be the bundle of all linear frames over a smooth manifold M, an arbitrarily given point of L(M), and a linear connection on M. Then the following result is well known: the horizontal subspace at the point may be written in terms of local coordinates of and Christoel's symbols defined by . This result is very fundamental on the study of the theory of connections. In this paper we show that the local expression of the horizontal subspace at the point u does not depend on the choice of a local coordinate system around the point , which is rarely seen.
bundle of linear frames;connection;horizontal subspace;
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