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- W2023714158 abstract "Let L(M) be the bundle of all linear frames over <TEX>$M,;u$</TEX> an arbitrarily given point of L(M), and <TEX>${nabla};:;mathfrak{X}(M);{times};mathfrak{X}(M);rightarrow;mathfrak{X}(M)$</TEX> a linear connection on L(M). Then the following results are well known: the horizontal subspace and the connection form at the point <TEX>$u$</TEX> may be written in terms of local coordinates of <TEX>$u;{epsilon};L(M)$</TEX> and Christoffel's symbols defined by <TEX>$nabla$</TEX>. These results are very fundamental on the study of the theory of connections. In this paper we show that the local expressions of those at the point <TEX>$u$</TEX> do not depend on the choice of a local coordinate system around the point <TEX>$u;{epsilon};L(M)$</TEX>, which is rarely seen. Moreover we give full explanations for the following fact: the covariant derivative on M which is defined by the parallelism on L(M), determined from the connection form above, coincides with <TEX>$nabla$</TEX>." @default.
- W2023714158 created "2016-06-24" @default.
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- W2023714158 date "2012-11-15" @default.
- W2023714158 modified "2023-09-26" @default.
- W2023714158 title "LINEAR CONNECTIONS IN THE BUNDLE OF LINEAR FRAMES" @default.
- W2023714158 doi "https://doi.org/10.14403/jcms.2012.25.4.731" @default.
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