Cohomogeneity one actions on the three-dimensional Einstein universe

The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe E in 1 , 2 , up to orbit equivalence. In a recent paper (Hassani in C R Acad Sci Paris Ser I 355:1133–1137, 2017. https://doi.org/10.1016/j.crma.2017.10.003 ), we studied the unique (u...

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Bibliographic Details
Published inGeometriae dedicata Vol. 206; no. 1; pp. 105 - 150
Main Authors Hassani, M., Ahmadi, P.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Subgroups
Topology
Universe
Einstein universe
57S25
Cohomogeneity one
Group action
Lorentzian geometry
37C85
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Summary:The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe E in 1 , 2 , up to orbit equivalence. In a recent paper (Hassani in C R Acad Sci Paris Ser I 355:1133–1137, 2017. https://doi.org/10.1016/j.crma.2017.10.003 ), we studied the unique (up to conjugacy) irreducible action of PSL ( 2 , R ) on E in 1 , 2 and we showed that the action is of cohomogeneity one. In the present paper, we determine all the subgroups of Conf ( E in 1 , 2 ) , up to conjugacy, acting reducibly and with cohomogeneity one on E in 1 , 2 . We show that any cohomogeneity one reducible action on E in 1 , 2 induces a fixed point in the 4-dimensional projective space R P 4 . Also, we describe all the codimension one induced orbits by these actions.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-019-00479-5