Abstract
Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.
Highlights
All manifolds considered in the paper are assumed to be finite dimensional, Hausdorff, second countable, without boundary and smooth
Of the present paper, we study the problem how a trivialization σ of P can induce a principal connection A(σ) in P. This problem is reflected in the concept of gauge natural operators A in the sense of [6] producing principal connections A(σ) : M → QP in P → M from trivializations σ of P
We prove that any gauge natural operator A in question is given by A(σ)(x) := [jx1σ]G
Summary
All manifolds considered in the paper are assumed to be finite dimensional, Hausdorff, second countable, without boundary and smooth (of class C∞). A principal connection in P is a right invariant section Γ : P → J1P of the first jet prolongation π01 : J1P → P of P → M .
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