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January, 2021 On the Chern–Moser–Weyl tensor of real hypersurfaces
Michael REITER, Duong Ngoc SON
J. Math. Soc. Japan 73(1): 77-98 (January, 2021). DOI: 10.2969/jmsj/82598259

Abstract

We derive an explicit formula for the well-known Chern–Moser–Weyl tensor for nondegenerate real hypersurfaces in complex space in terms of their defining functions. The formula is considerably simplified when applying to “pluriharmonic perturbations” of the sphere or to a Fefferman approximate solution to the complex Monge–Ampère equation. As an application, we show that the CR invariant one-form $X_{\alpha}$ constructed recently by Case and Gover is nontrivial on each real ellipsoid of revolution in $\mathbb{C}^3$, unless it is equivalent to the sphere. This resolves affirmatively a question posed by these two authors in 2017 regarding the (non-) local CR invariance of the $\mathcal{I}'$-pseudohermitian invariant in dimension five and provides a counterexample to a recent conjecture by Hirachi.

Funding Statement

The first author was supported by the Austrian Science Fund FWF-project P28873-N35. The second author was supported by the Austrian Science Fund FWF-project M 2472-N35.

Citation

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Michael REITER. Duong Ngoc SON. "On the Chern–Moser–Weyl tensor of real hypersurfaces." J. Math. Soc. Japan 73 (1) 77 - 98, January, 2021. https://doi.org/10.2969/jmsj/82598259

Information

Received: 8 May 2019; Revised: 28 August 2019; Published: January, 2021
First available in Project Euclid: 14 April 2020

Digital Object Identifier: 10.2969/jmsj/82598259

Subjects:
Primary: 32V40
Secondary: 53B25

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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