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Keywords:
second order geometry; stochastic calculus; connections; parallel transport
second order geometry; stochastic calculus; connections; parallel transport
Summary:
In this paper we prove that there is a bijective correspondence between connections of $H^2M$, the principal bundle of the second order frames of $M$, and stochastic parallel transport in the tangent space of $M$. We construct in a direct geometric way a prolongation of connections without torsion of $M$ to connections of $H^2M$. We interpret such prolongation in terms of stochastic calculus.
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