On the symmetry algebras of 5-dimensional CR-manifolds

Alexander Isaev; Boris Kruglikov

doi:10.1016/j.aim.2017.10.020

On the symmetry algebras of 5-dimensional CR-manifolds

Alexander Isaev, Boris Kruglikov^*

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface M and its symmetry algebra s one has either: (i) dim⁡s=15 and M is spherical (with Levi form of signature either (2,0) or (1,1) everywhere), or (ii) dim⁡s≤11 where dim⁡s=11 can only occur if on a dense open subset M is spherical with Levi form of signature (1,1). Furthermore, we construct a series of examples of pairwise nonequivalent CR-hypersurfaces with dim⁡s=11.

Original language	English
Pages (from-to)	530-564
Number of pages	35
Journal	Advances in Mathematics
Volume	322
DOIs	https://doi.org/10.1016/j.aim.2017.10.020
Publication status	Published - 15 Dec 2017

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abstract = "We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface M and its symmetry algebra s one has either: (i) dim⁡s=15 and M is spherical (with Levi form of signature either (2,0) or (1,1) everywhere), or (ii) dim⁡s≤11 where dim⁡s=11 can only occur if on a dense open subset M is spherical with Levi form of signature (1,1). Furthermore, we construct a series of examples of pairwise nonequivalent CR-hypersurfaces with dim⁡s=11.",

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AU - Isaev, Alexander

AU - Kruglikov, Boris

PY - 2017/12/15

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N2 - We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface M and its symmetry algebra s one has either: (i) dim⁡s=15 and M is spherical (with Levi form of signature either (2,0) or (1,1) everywhere), or (ii) dim⁡s≤11 where dim⁡s=11 can only occur if on a dense open subset M is spherical with Levi form of signature (1,1). Furthermore, we construct a series of examples of pairwise nonequivalent CR-hypersurfaces with dim⁡s=11.

AB - We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface M and its symmetry algebra s one has either: (i) dim⁡s=15 and M is spherical (with Levi form of signature either (2,0) or (1,1) everywhere), or (ii) dim⁡s≤11 where dim⁡s=11 can only occur if on a dense open subset M is spherical with Levi form of signature (1,1). Furthermore, we construct a series of examples of pairwise nonequivalent CR-hypersurfaces with dim⁡s=11.

KW - Gap phenomenon

KW - Lie algebras of infinitesimal CR-automorphisms

KW - Real hypersurfaces in complex space

UR - http://www.scopus.com/inward/record.url?scp=85033565658&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2017.10.020

DO - 10.1016/j.aim.2017.10.020

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SN - 0001-8708

VL - 322

SP - 530

EP - 564

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

On the symmetry algebras of 5-dimensional CR-manifolds

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