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Let L(M) be the bundle of all linear frames over a smooth manifold M, $u$ an arbitrarily given point of L(M), and ${\nabla}:\mathfrak{X}(M){\times}\mathfrak{X}(M){\rightarrow}\mathfrak{X}(M)$ a linear connection on M. Then the following result is well known: the horizontal subspace at the point $u$ may be written in terms of local coordinates of $u{\in}L(M)$ and Christoel's symbols defined by ${\nabla}$. 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 $u{\in}L(M)$, which is rarely seen.
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참고문헌 (4)
참고문헌 신청
S. Helgason / 1978 / Differential Geometry, Lie Groups and Symmetric Spaces / Academic Press
S. Kobayashi / 1963 / Foundation of Differential Geometry, Vol.I / Wiley-Interscience
I. Mogi / 1986 / Differential Geometry and Gauge Theory (in Japanese) / Kyoritsu Publ
Walter A. Poor / 1081 / Differential Geometric Structures / McGraw-Hill, Inc
S. Kobayashi / 1963 / Foundation of Differential Geometry, Vol.I / Wiley-Interscience
I. Mogi / 1986 / Differential Geometry and Gauge Theory (in Japanese) / Kyoritsu Publ
Walter A. Poor / 1081 / Differential Geometric Structures / McGraw-Hill, Inc
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