Geometriae Dedicata

, Volume 100, Issue 1, pp 123-155

First online:

Gromov's Centralizer Theorem

  • A. CandelAffiliated withDepartment of Mathematics, CSUN
  • , R. Quiroga-BarrancoAffiliated withDepartamento de Matemáticas, CINVESTAV-IPN

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We study the properties of rigid geometric structures and their relation with those of finite type. The main result proves that for a noncompact simple Lie group G acting analytically on a manifold M preserving a finite volume and either a connection or a geometric structure of finite type there is a nontrivial space of globally defined Killing vector fields on the universal cover \(\tilde M\) that centralize the action of G. Several appplications of this result are provided.

simple Lie groups finite type structures analytic actions