Local and infinitesimal rigidity of hypersurface embeddings

Abstract

We study local rigidity properties of holomorphic embeddings of real hypersurfaces in ${\mathbb{C}}^2$ into real hypersurfaces in ${\mathbb{C}}^3$ and show that infinitesimal conditions imply actual local rigidity in a number of (important) cases. We use this to show that generic embeddings into a hyperquadric in ${\mathbb{C}}^3$ are locally rigid.

35 pages