Local and infinitesimal rigidity of hypersurface embeddings

Abstract

We study local rigidity properties of holomorphic embeddings of real hypersurfaces in ℂ2 into real hypersurfaces in ℂ3 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 ℂ3 are locally rigid. © 2017 Amerian Mathematial Soiety.