Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

CR-hypersurfaces in a space with a pseudoconformal connection
HTML articles powered by AMS MathViewer

by Michael J. Markowitz PDF
Trans. Amer. Math. Soc. 276 (1983), 117-132 Request permission

Abstract:

In this paper we study a submanifold in a space with a pseudoconformal connection. We assume that the submanifold $M$ is so situated that it inherits the structure of a ${\text {CR}}$-hypersurface from the ambient space. $M$ then supports two natural Cartan connections, the normal pseudoconformal connection of Cartan-Chern-Tanaka and an induced pseudoconformal connection. Analogues of the Gauss-Codazzi equations are derived and applied to determine necessary and sufficient conditions for the equivalence of these connections.
References
  • D. Burns Jr. and S. Shnider, Real hypersurfaces in complex manifolds, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R.I., 1977, pp. 141–168. MR 0450603
  • Elie Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de l’espace de deux variables complexes, Ann. Mat. Pura Appl. 11 (1933), no. 1, 17–90 (French). MR 1553196, DOI 10.1007/BF02417822
  • S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
  • Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
  • Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886
  • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1963 original; A Wiley-Interscience Publication. MR 1393940
  • Noboru Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131–190. MR 589931, DOI 10.4099/math1924.2.131
  • S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), no. 1, 25–41. MR 520599
  • S. M. Webster, The rigidity of C-R hypersurfaces in a sphere, Indiana Univ. Math. J. 28 (1979), no. 3, 405–416. MR 529673, DOI 10.1512/iumj.1979.28.28027
  • Keizo Yamaguchi, Non-degenerate real hypersurfaces in complex manifolds admitting large groups of pseudo-conformal transformations. I, Nagoya Math. J. 62 (1976), 55–96. MR 430296
  • Kentaro Yano and Yosio Mutô, Sur la théorie des espaces à connexion conforme normale et la géométrie conforme des espaces de Riemann, J. Fac. Sci. Imp. Univ. Tokyo Sect. I. 4 (1941), 117–169 (French). MR 0005710
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 32F25, 53B25
  • Retrieve articles in all journals with MSC: 32F25, 53B25
Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 117-132
  • MSC: Primary 32F25; Secondary 53B25
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0684496-0
  • MathSciNet review: 684496