The Schwarzian derivative and Möbius equation on strictly pseudo-convex CR manifolds. (English) Zbl 1392.32016

Summary: The notion of Schwarzian derivative for locally univalent holomorphic functions on complex plane was generalized for conformal diffeomorphisms by B. Osgood and D. Stowe [Duke Math. J. 67, No. 1, 57–99 (1992; Zbl 0766.53034)]. We shall identify a tensor that may serve as an analogue of the Schwarzian of Osgood and Stowe for CR mappings and then use the tensor to define and study the CR Möbius transformations and metrics of pseudohermitian manifolds. We shall establish basic properties of the CR Schwarzian and a local characterization of the CR spherical manifolds in terms of the fully integrability of the CR Möbius equation. In another direction, we shall prove two rigidity results for the Möbius changes of metrics on compact CR manifolds.


32V05 CR structures, CR operators, and generalizations
32V99 CR manifolds


Zbl 0766.53034
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