Geodesic
Structural equations of the Cartan connection with the curvature-torsion quasi-tensor
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 130-138

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Using a two-tier principal connection, we construct an interpretation of the Cartan connection, which is not a connection in the principal bundle, and obtain its structural equations in two forms. We prove that in the classical structural equations, the curvature-torsion object is a tensor, which becomes a quasi-tensor under reduction of the equations.
Keywords: principal bundle, extended principal bundle, Laptev's lemma, semiholonomy, Cartan–Laptev theorem, curvature tensor, gluing, curvature-torsion tensor.
Mots-clés : principal connection, Cartan's connection 
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     author = {Yu. I. Shevchenko and E. V. Skrydlova},
     title = {Structural equations of the {Cartan} connection with the curvature-torsion quasi-tensor},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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Yu. I. Shevchenko; E. V. Skrydlova. Structural equations of the Cartan connection with the curvature-torsion quasi-tensor. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 130-138. http://geodesic.mathdoc.fr/item/INTO_2021_203_a10/