, Volume 344, Issue 1, pp 185-211
Date: 04 Nov 2008

Local embeddability of CR manifolds into spheres

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Abstract

In this paper we solve local CR embeddability problem of smooth CR manifolds into spheres under a certain nondegeneracy condition on the Chern–Moser’s curvature tensor. We state necessary and sufficient conditions for the existence of CR embeddings as finite number of equations and rank conditions on the Chern–Moser’s curvature tensors and their derivatives. We also discuss the rigidity of those embeddings.