 

Hikaru Yamamoto
Special Lagrangians and Lagrangian selfsimilar solutions in cones over toric Sasaki manifolds view print


Published: 
June 26, 2016 
Keywords: 
Toric Sasaki manifold, special Lagrangian, selfsimilar solution 
Subject: 
Primary 53C42, Secondary 53C21, 53C25, 53C44 


Abstract
We construct some examples of special Lagrangian submanifolds
and Lagrangian selfsimilar solutions in almost CalabiYau cones over toric Sasaki manifolds.
For example, for any integer g≧ 1,
we can construct a real 6dimensional CalabiYau cone M_{g}
and a 3dimensional special Lagrangian submanifold F^{1}_{g}:L_{g}^{1}→ M_{g} which is diffeomorphic to Σ_{g} × R
and a compact Lagrangian selfshrinker F^{2}_{g}:L_{g}^{2}→ M_{g} which is
diffeomorphic to Σ_{g} × S^{1}, where Σ_{g} is a closed surface of genus g.


Author information
Department of Mathematics, Faculty of Science, Tokyo University of Science, 13, Kagurazaka, Shinjukuku, Tokyo 1628601, Japan
hyamamoto@rs.tus.ac.jp

