Vector fields and connections on $TM$

Anton Dekrét

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

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 $J^{1} Y \to X$ .

Displaying similar documents to “Vector fields and connections on T M ”

Prolongation of second order connections to vertical Weil bundles

On the prolongation of vertical connections.

Some natural operations between connections on fibred manifolds

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