Geometry Colloquium: Homogeneous Lagrangian submanifolds of SL(2,R)xSL(2,R) (Mateo Anarella)

Time： 16:30-17:30

Place：Faculty of Science Building  #4, Room 4-409

Speaker：Mateo Anarella（Hokkaido University）

Title：Homogeneous Lagrangian submanifolds of SL(2,R)xSL(2,R)

Abstract：In this talk we will analyze the nearly Kähler structure of the pseudo-Riemannian manifold SL(2,R)×SL(2,R). As an analogue of S3 × S3 , we can define a natural almost product structure P, compatible with the nearly Kähler metric, by swapping the vector fields tangent to each component of SL(2,R) × SL(2,R). Given a Lagrangian submanifold M, we will study the different forms the restriction P|TM can take. We will give a classification result for extrinsically homogeneous Lagrangian submanifolds of SL(2,R) × SL(2,R). We will study two different ways that we can obtain this result, analyzing the pros and cons of each method.