Vector fields and connections on $TM$

Anton Dekrét

Displaying similar documents to “Vector fields and connections on $TM$”

Prolongation of second order connections to vertical Weil bundles

Antonella Cabras, Ivan Kolář (2001)

Archivum Mathematicum

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$ . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$ -field for another Weil algebra $B$ and of its $A$ -prolongation.

On the prolongation of vertical connections.

Győry, Ákos (2000)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr

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Given a fibered manifold $Y \to X$ , a 2-connection on $Y$ means a section $J^{1} Y \to J^{2} Y$ . The authors determine all first order natural operators transforming a 2-connection on $Y$ and a classical linear connection on $X$ into a connection on $J^{1} Y \to Y$ . (The proof implies that there is no first order natural operator transforming 2-connections on $Y$ into connections on $J^{1} Y \to Y$ .) Using this result, the authors deduce several properties of characterizable connections on $J^{1} Y \to X$ .