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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.

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Rigidity of pseudoconformal connections
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by Michael Markowitz and Roger Schlafly PDF
Trans. Amer. Math. Soc. 276 (1983), 133-135 Request permission

Abstract:

Let ${M^{2n - 1}}(n \geqslant 3)$ be a strictly pseudoconvex abstract ${\text {CR}}$-hypersurface ${\text {CR}}$-immersed in the unit sphere in ${{\mathbf {C}}^N}$. We show that the pseudoconformal connection induced on $M$ by the standard flat connection agrees with the intrinsic normal connection of Cartan-Chern-Tanaka if and only if $M$ is pseudoconformally flat. In this case $M$ is a piece of the transverse intersection of ${S^{2N - 1}}$ with a complex $n$-plane in ${{\mathbf {C}}^N}$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 133-135
  • MSC: Primary 32F25; Secondary 53B15
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0684497-2
  • MathSciNet review: 684497