New York Journal of Mathematics
Volume 21 (2015) 465-484


Takayuki Moriyama

Special Legendrian submanifolds in toric Sasaki-Einstein manifolds

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Published: July 1, 2015
Keywords: Legendrian submanifolds, Sasaki-Einstein manifolds
Subject: Primary 53C25, 53C40; Secondary 53C38

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

Author information

Department of Mathematics, Mie University, Mie 514-8507, Japan