Inflexible \(CR\) submanifolds (Q2412540)

The authors consider \textit{abstract} compactly supported deformations of CR submanifolds \((M,HM,J)\) of \(\mathbb{C}^N,\) of arbitrary CR dimension \(n\) and CR codimension \(d\). They call \textit{flexible} those admitting a compactly supported deformation \(\{(M_a,HM_a,J_a)\}_{a{>}0}\), such that the abstract CR manifold \((M_a,HM_a,J_a)\) is not globally embeddable into a Euclidean complex space for arbitrarily small \(a{>}0.\) They show that \(2\)-pseudoconcave generic CR submanifolds of \(\mathbb{C}^{n{+}d}\) are inflexible.