Characteristic rank of canonical vector bundles over oriented Grassmann manifolds G˜3,n

We determine the characteristic rank of the canonical oriented vector bundle over G˜3,n for all n≥3, and as a consequence, we obtain the affirmative answer to a conjecture of Korbaš and Rusin. As an application of this result, we calculate the Z2-cup-length for a new infinite family of manifolds G˜3,n. This result confirms the corresponding claim of Fukaya's conjecture.