On Cohomogeneity One Linear Actions On Pseudo-euclidean Space\n \ℝ^p,q

2019/08/14 by P. Ahmadi, Ahmadi, Parviz, Salim Safari +2
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1908.05083

openalex publication_date 2019/08/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study cohomogeneity one isometric linear actions\non the p+q-dimensional pseudo-Euclidean space \ℝ^p,q. It is\nproved that the natural isometric action of the nilpotent factor of an Iwasawa\ndecomposition of SO(p,q) is not of cohomogeneity one. The orbits of\ncohomogeneity one actions of some subgroups of a maximal parabolic subgroup of\nthe isometry group of \ℝ^p,q are determined and it is proved that\nthere exist cohomogeneity one isometric actions on \ℝ^p,q which are\norbit-equivalent on the complement of a p-dimensional degenerate subspace\n mathbbW^p of \ℝ^p,q and not orbit-equivalent on mathbbWp.\n

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