Mathematische Annalen

, Volume 344, Issue 1, pp 185–211

Local embeddability of CR manifolds into spheres


DOI: 10.1007/s00208-008-0302-8

Cite this article as:
Kim, SY. & Oh, JW. Math. Ann. (2009) 344: 185. doi:10.1007/s00208-008-0302-8


In this paper we solve local CR embeddability problem of smooth CR manifolds into spheres under a certain nondegeneracy condition on the Chern–Moser’s curvature tensor. We state necessary and sufficient conditions for the existence of CR embeddings as finite number of equations and rank conditions on the Chern–Moser’s curvature tensors and their derivatives. We also discuss the rigidity of those embeddings.

Mathematics Subject Classification (2000)

Primary 32V3032V20Secondary 53B2535N10

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematical EducationKangwon National UniversityKangwon-doSouth Korea
  2. 2.School of MathematicsKorea Institute for Advanced StudySeoulSouth Korea