报告题目【Lagrangian submanifolds of the complex hyperbolic quadric】
时间：2019年05月09日(星期四)下午14:30
地点：旗山校区理工北楼601报告厅
主讲：比利时Leuven大学博士，Anne Wijffels
主办：数学与信息学院、福建省分析数学及应用重点实验室
参加对象：数学相关专业教师及研究生
报告人简介：Anne Wijffels，比利时Leuven大学博士，主要研究仿射微分几何。
报告摘要：The complex hyperbolic quadric Q^{n} is the complex hypersurface of complex anti-de Sitter space CH^{n+1}_{1}, given in homogeneous coordinates by the equation -z_{0}^{2}-z_{1}^{2}+…+z_{n+1}^{2}= 0. This manifold inherits a Kaehler structure from the complex anti-de Sitter space and the shape operators define almost product structures on Q^{n}. Its curvature can relatively easy be described in terms of these two structures.
Moreover, the Grassmannian Q^{n} is the natural target space when considering the Gauss map of a spacelike hypersurface of anti-de Sitter space H^{n+1}_{1}(-1).In fact, such Gauss maps are related to Lagrangian submanifolds of Q^{*n}.
Therefore we are particularly interested in the Lagrangian immersions in the complex hyperbolic quadric. In particular, we classify all the minimal Lagrangians with constant sectional curvature.
The 1-dimensional quadric Q^{*1} is isometric to the 2-dimensional hyperbolic space H^{2}. The 2-dimensional quadric Q^{*2} is isometric to the Riemannian product of hyperbolic spaces H^{2}. Remark that such a relation does not exist for higher dimensions.
