中科院数学与系统科学研究院
数学研究所
拓扑研讨班
报告人： 陈 亮 副教授（东北师范大学）
题 目：Legendrian Dualities and Geometry of Submanifolds
时 间：2021.09.08（星期三），13 :30-14 :30
地 点：腾讯会议：110 766 998
摘 要：Singularity and degeneracy destroy the structure of manifolds and give rise to essential difficulties in researching the deteriorative manifolds. Thus, it is crucial to develop new methods for investigating the singular or degenerate manifolds. By characterizing the inner connection between pseudo spheres in semi-Euclidean space, the Legendrian dualities are effective methods developed by L. Chen and Izumiya in 2009 for studying the submanifolds in non-flat space. Specially, the Legendrian duality is applicable for studying the singular or degenerate submanifolds. In this talk, we will introduce the basic notions of Legendrian dualities. As their applications, using the singularity theory of mappings, we investigate the topological and geometrical properties of the (singular or degenerate) submanifolds immersed in non-flat space from the viewpoint of duality.
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