Rigid Levi degenerate hypersurfaces with vanishing CR-curvature

Alexander Isaev

doi:10.1016/j.jmaa.2019.01.029

Rigid Levi degenerate hypersurfaces with vanishing CR-curvature

Alexander Isaev

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We continue the study, initiated in our earlier article, of a class of rigid hypersurfaces in C ³ that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of the earlier paper and give a complete description of the class. Surprisingly, the answer is expressed in terms of solutions of several well-known differential equations, in particular, the equation characterizing conformal metrics of constant negative curvature and a nonlinear ∂¯-equation.

Original language	English
Pages (from-to)	782-792
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	474
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2019.01.029
Publication status	Published - 15 Jun 2019

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abstract = " We continue the study, initiated in our earlier article, of a class of rigid hypersurfaces in C 3 that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of the earlier paper and give a complete description of the class. Surprisingly, the answer is expressed in terms of solutions of several well-known differential equations, in particular, the equation characterizing conformal metrics of constant negative curvature and a nonlinear ∂¯-equation.",

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AB - We continue the study, initiated in our earlier article, of a class of rigid hypersurfaces in C 3 that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of the earlier paper and give a complete description of the class. Surprisingly, the answer is expressed in terms of solutions of several well-known differential equations, in particular, the equation characterizing conformal metrics of constant negative curvature and a nonlinear ∂¯-equation.

KW - CR-curvature

KW - Rigid hypersurfaces

KW - The Monge equation

KW - The complex Monge–Ampère equation

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Rigid Levi degenerate hypersurfaces with vanishing CR-curvature

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