Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations

Abstract

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we show higher order infinitesimal conditions can be used to give a characterization of local rigidity.

References in corpus (5)

• The equivalence and the embedding problems for CR-structures of any codimension
• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• Homotopy equivalence for proper holomorphic mappings
• Local and infinitesimal rigidity of hypersurface embeddings
• Topological Aspects of Holomorphic Mappings of Hyperquadrics from ${\mathbb{C}}^2$ to ${\mathbb{C}}^3$

Cited by in corpus (3)

• On CR maps from the sphere into the tube over the future light cone
• Deformations of CR maps and applications
• On highly degenerate CR maps of spheres