Mathematical Sciences: Geometry and Analysis on CR Manifolds

李约翰将继续他的研究柯西黎曼 流形他将调查某些人 伪厄米流形上的曲率和挠张量可以 通过适当选择CR结构和接触， form. 要考虑的主要问题是：1）CR Yamabe 要求切触形式为常数标量的问题 曲率; 2）选择接触形式，其中韦伯斯特 Ricci张量是Levi形式的标量倍数; 3）到 确定哪些CR流形允许满足以下两个条件的接触形式 （4）确定在何种条件下， CR结构可以变化，以实现扭转消失， 常数标量曲率

John Lee will continue his studies of Cauchy Riemann manifolds. He will investigate the ways in which certain curvature and torsion tensors on a pseudohermitian manifold can be simplified by appropriate choice of CR structure and contact form. The principal problems to be considered are 1) the CR Yamabe problem which asks for a contact form with constant scalar curvature; 2) to choose a contact form for which the Webster Ricci tensor is a scalar multiple of the Levi form; 3) to determine which CR manifolds admit contact forms satisfying both previous conditions; 4) to determine conditions under cwhich the CR structure can be varied to achieve vanishing torsion and constant scalar curvature.