We show that every toric Sasaki-Einstein manifold $S$ admits a special Legendrian submanifold $L$ which arises as the link ${ \rm fix}(\tau)\cap S$ of the fixed point set ${ \rm fix}(\tau)$ of an anti-holomorphic involution $\tau$ on the cone $C(S)$. In particular, an irregular toric Sasaki-Einstein manifold $S^{ 2}\times S^{ 3}$ has a special Legendrian torus $S^{ 1}\times S^{ 1}$. Moreover, we also obtain a special Legendrian submanifold in $\sharp m(S^{ 2}\times S^{ 3})$ for each $m\ge 1$.
Categories: math.DG