Regularity of rigid CR hypersurfaces in a sphere

Abstract

Abstract. Let M be a germ of a smooth CR manifold of hypersurface type of dimension 2n + 1 in a sphere S of dimension 2N + 1 with n < N. In this paper, we show that if M is rigid and if N − n < n/2, then there exists a complex manifold V of (complex) dimension n + 1 intersecting S transversally such that M = S ∩ V . As a consequence, we show that M is real analytic.