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. 2021;7(3-4):25.
doi: 10.1007/s40627-021-00083-y. Epub 2021 Jul 15.

Compact homogeneous Leviflat CR-manifolds

A R Al-Abdallah  1 , B Gilligan  1
Affiliations

Compact homogeneous Leviflat CR-manifolds

A R Al-Abdallah et al. Complex Analysis Synerg. 2021.

Abstract

We consider compact Leviflat homogeneous Cauchy-Riemann (CR) manifolds. In this setting, the Levi-foliation exists and we show that all its leaves are homogeneous and biholomorphic. We analyze separately the structure of orbits in complex projective spaces and parallelizable homogeneous CR-manifolds in our context and then combine the projective and parallelizable cases. In codimensions one and two, we also give a classification.

Keywords: Dense leaves; Homogeneous CR-manifolds; Levi-foliation; Leviflat.

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Conflict of interest statement

Conflict of interestOn behalf of all authors, the corresponding author states that there is no conflict of interest.

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