Mathematical Sciences: CR Geometry and Several Complex Variables

霍华德·雅各布维茨将继续他在柯西黎曼几何和几个复杂变量方面的研究。这是一个重要的领域，涉及复变理论的拓扑和分析方面。雅各布维茨将运用几何技术来解决正在研究的问题。整个研究的一个主要主题将是柯西黎曼结构的嵌入问题。研究的目的之一是证明更一般的Newlander-Nirenberg定理的边界版本，从而获得更一般的CR结构的局部可嵌入性的条件。另一个目标是推广一个局部但非全局可嵌入的CR结构的例子。Jacobowitz还将继续研究费费曼螺旋的普遍性及其与零卡坦曲率点的关系。最后一个主题是研究某些奇异二维度量的共形类。在这里，他将与每个度规关联一个复向量场，并研究向量场的齐次可解性。

Howard Jacobowitz will continue his work in Cauchy Riemann geometry and several complex variables. This an important area which involves both topological and analytic aspects of complex variable theory. Jacobowitz will bring geometric techniques to bear on the problems under investigation. A major theme throughout the research will be embedding problems for Cauchy Riemann structures. One aim of the research is to prove a more general boundary version of the Newlander-Nirenberg theorem and thereby obtain conditions for the local embeddability of more general CR structures. Another objective is to generalize an example of a locally but not globally embeddable CR structure. Jacobowitz will also continue his investigations of the prevalence of Fefferman spirals and their relations to points of zero Cartan curvature. A final topic is the study of the conformal class of certain singular two-dimensional metrics. Here he will associate with each metric a complex vector field and investigate the homogeneous solvability of the vector field.