Mathematical Sciences: CR Manifolds and Pseudo-Riemannian Geometry

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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.