Austere Submanifolds in Complex Projective Space

For an arbitrary submanifold $M\subset \mathbb{C}{P}^n$ we determine conditions under which it is austere, i.e., the normal bundle of $M$ is special Lagrangian with respect to Stenzel’s Ricci-flat K"ahler metric on $T\mathbb{C}{P}^n$. We also classify austere surfaces in $\mathbb{C}{P}^n$.