Cohomogeneity one actions on the three-dimensional Einstein universe

2018/10/01 by Masoud Hassani, Hassani, Masoud, Parviz Ahmadi +1
Mathematics · #37C85 #57S25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:37C85 #msc:57S25

paper · pdf · doi:10.48550/arxiv.1810.00575

arxiv created 2018/10/01 · arxiv updated 2018/10/02

Abstract

The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe Ein^1;2 , up to orbit equivalence. In a recent paper [21], we studied the unique (up to conjugacy) irreducible action of PSL(2; ℝ) on Ein^1;2 and we showed that the action is of cohomogeneity one. In the present paper, we determine all the subgroups of Conf(Ein^1;2), up to conjugacy, acting reducibly and with cohomogeneity one on Ein^1;2. We show that any cohomogeneity one reducible action on Ein^1;2 induces a fixed point in the 4-dimensional projective space ℝ ℙ⁴. Also, we describe all the codimension one induced orbits by these actions

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