Differential geometric connection of finite order on composite manifold, infinitesimal polygons and geometric interpretation of Bianchi identity (Q1201391)
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scientific article; zbMATH DE number 97855
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| English | Differential geometric connection of finite order on composite manifold, infinitesimal polygons and geometric interpretation of Bianchi identity |
scientific article; zbMATH DE number 97855 |
Statements
Differential geometric connection of finite order on composite manifold, infinitesimal polygons and geometric interpretation of Bianchi identity (English)
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17 January 1993
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Let \(\Gamma\) be a higher order connection in the sense of \textit{V. V. Vagner} [Tr. Semin. Vektorn. Tensorn. Anal., Prilozh. Geom. Mekh. Fiz. 8, 11--72 (1950; Zbl 0041.29801)]. The author deduces several properties of the infinitesimal holonomy group of \(\Gamma\). In particular, his approach leads to a geometric interpretation of the Bianchi identity of \(\Gamma\).
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higher order connection
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infinitesimal holonomy group
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