HORIZONTAL SUBSPACES IN THE BUNDLE OF LINEAR FRAMES

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 4,  2012, pp.513-517
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.4.513
Title & Authors
HORIZONTAL SUBSPACES IN THE BUNDLE OF LINEAR FRAMES
Park, Joon-Sik;

Abstract
Let L(M) be the bundle of all linear frames over a smooth manifold M, $\small{u}$ an arbitrarily given point of L(M), and $\small{{\nabla}:\mathfrak{X}(M){\times}\mathfrak{X}(M){\rightarrow}\mathfrak{X}(M)}$ a linear connection on M. Then the following result is well known: the horizontal subspace at the point $\small{u}$ may be written in terms of local coordinates of $\small{u{\in}L(M)}$ and Christoel's symbols defined by $\small{{\nabla}}$. 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 $\small{u{\in}L(M)}$, which is rarely seen.
Keywords
bundle of linear frames;connection;horizontal subspace;
Language
English
Cited by
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