Induction of Geometric Actions

Scot Adams

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We prove that, in some situations, an induced action from a normal subgroup preserves a geometric structure. Combined with known geometric rigidity results, this result implies certain rigidity statements concerning the full diffeomorphism group of a manifold. It also provides many examples of actions on Lorentz manifolds. Combining these with a small number of well-known actions, we get the full list of connected, simply connected Lie groups admitting a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold. We give an example of a connected nilpotent Lie group with no complicated action on a Lorentz manifold. We show that, if a connected Lie group has a normal closed subgroup isomorphic to a (two-dimensional) cylinder, then it admits a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold.

Original languageEnglish (US)
Pages (from-to)91-112
Number of pages22
JournalGeometriae Dedicata
Volume88
Issue number1-3
DOIs
StatePublished - Dec 1 2001

Keywords

  • Isometrics
  • Lorentz manifolds
  • Transformation groups

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