We study the Saito-Ikeda infinitesimal invariant of the cycle defined by curves in their Jacobians using rank $k+1$ vector bundles. We give a criterion for which the higher cycle class map is not trivial. When $k = 2$, this turns out to be strictly linked to the Petri map for vector bundles. In this case we can improve a result of Ikeda: an explicit construction on a curve of genus $g \geq 10$ shows the existence of a non trivial element in the higher Griffiths group.
"Infinitesimal invariant and vector bundles." Nagoya Math. J. 186 95 - 118, 2007.