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A restriction on proper group actions on homogeneous spaces of reductive type

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Abstract

Let \(L\) be a reductive subgroup of a reductive Lie group \(G\). Let \(G/H\) be a homogeneous space of reductive type. We provide a necessary condition for the properness of the action of \(L\) on \(G/H\). As an application we give examples of spaces that do not admit standard compact Clifford-Klein forms.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710, Olsztyn, Poland

    Maciej Bocheński

  2. Department of Geodesy and Land Management, University of Warmia and Mazury, Prawocheńskiego 15, 10-720, Olsztyn, Poland

    Marek Ogryzek

Authors
  1. Maciej Bocheński
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  2. Marek Ogryzek
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Correspondence to Maciej Bocheński.

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Bocheński, M., Ogryzek, M. A restriction on proper group actions on homogeneous spaces of reductive type. Geom Dedicata 178, 405–411 (2015). https://doi.org/10.1007/s10711-015-0063-y

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  • DOI: https://doi.org/10.1007/s10711-015-0063-y

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