Mathematical Sciences: Geometry and Analysis on CR Manifolds

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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.