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The Chern Connection of a $$(J^{2}=\pm 1)$$(J2=±1)-Metric Manifold of Class $${\mathcal {G}}_{1}$$G1
Mediterranean Journal of Mathematics, 2018F. Etayo +2 more
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A characterization of the Chern and Bernwald connections
1996Let \(M\) be a smooth manifold and \(\pi:TM\to M\) its tangent bundle. The vertical subbundle \(V\subset T(TM)\) is \(\text{Ker} D\pi\) and a supplement of it is a horizontal bundle. A linear connection in \(V\) is good if it can be canonically prolonged to \(TM\).
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Chern–Simons forms for ℝ-linear connections on Lie algebroids
International Journal of Mathematics, 2018This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.
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Shen's L-process on the Chern connection
2023Faghfouri, Morteza, Jazer, Nadereh
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The chern-simons theory and quantized moduli spaces of flat connections
2007Anton Yu. Alekseev, Volker Schomerus
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