Mathematical Sciences: CR Manifolds and Pseudo-Riemannian Geometry

丽莎科赫将开展柯西黎曼几何的研究 使用伪黎曼几何的技术。她将学习 一些特殊的非平坦CR流形上链的行为。 她的研究还将涉及一个更普遍的调查， 伪黎曼流形与CR的对应 流形在这种情况下，她将研究这样一个 广义链状曲线上的对应 链的研究将使用一个结构的费曼 将它们与伪黎曼曲面上的光线联系起来 歧管要研究的主要例子之一是 螺旋链由于弗罗曼。她还将研究 Sparling对共形曲率的限制 零测地线的

Lisa Koch will carry out research in Cauchy Riemann geometry using techniques of pseudo-Riemannian geometry. She will study the behavior of chains on some specific non-flat CR manifolds. Her research will also involve investigations of a more general correspondence between pseudo-Riemannian manifolds and CR manifolds. In this context she will study the effect of such a correspondence on generalized chain-like curves. The study of chains will use a construction of Fefferman which connects them to light rays on a pseudo-Riemannian manifold. One of the main examples to be studied is the important spiraling chain due to Fefferman. She will also study the effect Sparling's restriction on conformal curvature has on the behavior of null geodesics.