Mathematical Sciences: RUI: Geometry of Submanifolds

主要研究员将继续他的研究子流形的简单连接常曲率流形使用的技术李球几何。特别是他将试图给一个分类的紧张和杜宾子流形。研究员还将继续让本科生参与他的研究，从而为他们提供研究生学习的坚实背景。单连通常曲率流形是欧氏空间、球面和双曲空间。这些流形是非常特殊的，并且可以作为微分几何中许多问题的测试案例。主要研究者将尝试对这些流形中的所有子流形或曲面进行分类，这些子流形是拉紧的或刚性的。

The principal investigator will continue his study of submanifolds of the simply connected constant curvature manifolds using the techniques of Lie sphere geometry. In particular he will attempt to give a classification of the taut and Dupin submanifolds. The investigator will also continue to involve undergraduate students in his research thus providing them with a solid background for graduate study. The simply connected constant curvature manifolds are Euclidean space, the sphere, and hyperbolic space. These manifolds are very special and serve as test cases for many questions in differential geometry. The principal investigator will attempt to classify all submanifolds or surfaces in these manifolds which are taut or rigid.