Representations of Discrete Groups and Geometric Topology on Manifoldss, Josai University

This is a survey on the author's recent work [22] and a pre-report on [23]. We show a method of constructing an in-variant Lagrangian mean curvature flow in a Calabi-Yau manifold with the use of generalized perpendicular symmetries. We also show a way to construct special Lagrangian submanifolds as a special case of our method. We use moment maps of the actions of Lie groups, which are not necessarily abelian. By our method, we construct a non-trivial examples of special Lagrangian submanifolds in the cotangent bundle of the n-sphere T* Sn and a self-similar solution of a Lagrangian mean curvature flow in Cn