Topology and geometry of 3-dimensional pseudo-gradient CR Yamabe solitons with zero torsion
陳志偉博士台大數學 下午 2:30–4:00 鴻經館 107 室Abstract:
It has been known from the 70’s that all closed orientable 3-manifolds admit CR structures. Among all these manifolds, we prove that only sphere and the lens spaces may admit non-trivial torsion-free pseudo-gradient CR Yamabe soliton structures.
For a non-trivial complete soliton, which always admits a Riemannian metric with indefinite curvature sign, we show that it must be diffeomorphic to the Euclidean space if it is simply-connected, torsion-free and has certain bound on the Webster curvature.
This is a joint work with Huai-Dong Cao and Shu-Cheng Chang.