Special Lagrangians and Lagrangian self-similar solutions in cones over toric Sasaki manifolds

Details Special Lagrangians and Lagrangian self-similar solutions in cones over toric Sasaki manifolds Special Lagrangians and Lagrangian self-similar solutions in cones over toric Sasaki manifolds

2012-03-18

arxiv.org/abs/1203.3934v1

Mathematics

Differential Geometry

36 pages, 19 figures. arXiv admin note: text overlap with arXiv:math/0701122

Scientific paper

We construct some examples of special Lagrangian submanifolds and Lagrangian self-similar solutions in (almost) Calabi--Yau cones of toric Sasaki manifolds. These special Lagrangian submanifolds in cones are extensions of previously known examples constructed in the complex space C^n by Joyce, and the examples of Lagrangian self-similar solutions in cones are extensions of those constructed in C^n by Joyce, Lee and Tsui. Furthermore, for any integer g, we construct three dimensional special Lagrangian submanifolds which are diffeomorphic to the product of the real line R and the closed surface of genus g, and we also construct compact Lagrangian self-similar solutions which are diffeomorphic to the product of the circle S^1 and the closed surface of genus g.

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