Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G'\subseteq G$ to be a pair of Lie groups that act on $Y\subseteq X$, respectively. We call a differential operator $D$ between the space of smooth sections for a $G$-equivariant vector bundle over $X$ and that for a $G'$-equivariant vector bundle over $Y$ a differential symmetry breaking operator (differential SBO for short) if $D$ is $G'$-intertwining.

In this talk we shall discuss the classification and construction of differential SBOs $D$ from a line bundle to a vector bundle over real projective spaces.