Mathematical Sciences: Research in Several Complex Variables

主要研究人员将研究将三维CR流形嵌入到欧氏空间的问题。他将在模空间中讨论CR流形的可嵌入性问题，并试图通过将该问题与凸域边界上的圆作用联系起来来描述那些可嵌入的CR流形。特别是，他将试图理解当CR结构被扰动时，圆的作用是如何变化的。CR流形是复数空间几何中一种重要的抽象结构。为了更好地理解这些空间，人们想把它们想象成通常欧几里得空间的子空间，例如我们日常的三维空间。首席研究人员将尝试描述这种可视化或“隐蔽性”何时成为可能。

The principal investigator will study the problem of imbedding three dimensional CR manifolds into Euclidean space. He will approach the problem of imbeddibility of CR manifolds in terms of a moduli space and attempt to describe those CR manifolds which are imbeddible by relating the problem to a circle action on the boundary of a convex domain. In particular he will try to understand how the circle action changes when the CR structure is perturbed. A CR manifold is an important abstract structure in the geometry of spaces of complex numbers. To better understand these spaces one would like to visualize them as subspace of the usual Euclidean space such as our everyday three dimensional space. The principal investigator will attempt to describe when this visualization or "imbedibility" is possible.