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Double linear connections. (English) Zbl 0762.53014

The notion of a \(DL\) (i.e. double vector) space was introduced by the author in Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 88, Math. 26, 9-25 (1987; Zbl 0701.58004). In the present paper double linear connections on \(DL\) fibrations (i.e. on double vector bundles) are investigated as analogues of linear connections on vector bundles. \(DL\) fibrations are associated with principal bundles of double linear frames. A \(DL\) fibration turns out to be a Whitney sum of its underlying vector fibrations. It is shown that a \(DL\) connection induces linear connections on the underlying vector fibrations. Finally double linear connections are characterized by means of double linear vector fields and double linear one parameter groups.

MSC:

53C05 Connections (general theory)

Citations:

Zbl 0701.58004
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References:

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