Abstract
The concepts of first order projective deformation, biholomorphic equivalence, and equivalence of induced Cauchy-Riemann structure are all equivalent for real analytic hypersurfaces in complex projective space. Studying the first concept leads to a realization of the Cauchy-Riemann structure bundle as a submanifold of the projective group. The Chern-Moser connection on this bundle can then be given in terms of the Maurer-Cartan form of the projective group, and equations analogous to the Gauss equations of Euclidean geometry give the Chern-Moser invariants.
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CARTAN, E.: Sur le problème général de la déformation, C.R. Congrès Strasbourg (1920) 397–406, (or Oeuvres III, 1, 539–548).
—: Sur le géométrie pseudo-conforme des hypersurfaces de deux variables complexes, Ann. Math. Pura Appl. (4)11 (1932) 17–90, (or Oeuvres II, 2, 1231–1304).
——: Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945.
CHERN, S.S. and MOSER, J.:Real hypersurfaces in complex manifolds, Acta Math.133 (1974) 219–271.
JENSEN, G.R.: Deformation of submanifolds of homogeneous spaces, J. Diff. Geom.16 (1981), No. 2.
KOBAYASHI, S.: Transformation groups in differential geometry, Springer-Verlag, New York, 1972.
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Research supported by the National Science Foundation under Grant Number MCS-8103370.
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Jensen, G.R. Projective deformation and biholomorphic equivalence of real hypersurfaces. Ann Glob Anal Geom 1, 1–34 (1983). https://doi.org/10.1007/BF02329737
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DOI: https://doi.org/10.1007/BF02329737