Orientable minimal submanifolds of low index in the sphere

In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only closed and connected $(2m-2)$-dimensional orientable minimal submanifolds in ${\mathbb{S}}^{2m}$ of index less than or equal to $2m+1$ are the totally geodesic spheres.