Remarks on minimal rational curves on moduli spaces of stable bundles

Let M be the moduli space of stable bundles of rank 2 and with fixed determinant $\mathcal{L}$ of degree d on a smooth projective curve C of genus g>= 2. When g=3 and d is even, we prove, for any point [W]\in M, there is a minimal rational curve passing through [W], which is not a Hecke curve. This complements a theorem of Xiaotao Sun.