We show every toric Sasaki-Einstein manifold S admits a special Legendrian submanifold L which arises as the link fix(τ)∩ S of the fixed point set fix(τ) of an anti-holomorphic involution τ on the cone C(S). In particular, we obtain a special Legendrian torus S¹× S¹ in an irregular toric Sasaki-Einstein manifold which is diffeomorphic to S²× S³. Moreover, there exists a special Legendrian submanifold in ♯m(S²× S³) for each m≧1.

This work was partially supported by GCOE `Fostering top leaders in mathematics', Kyoto University and by Grant-in-Aid for Young Scientists (B) #21740051 from JSPS