Abstract
We give a new version of the Gromov’s centralizer theorem in the case of semisimple Lie group actions and arbitrary rigid geometric structures of algebraic type.
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Amores, A.M.: Vector fields of a finite type G-structures. J. Differ. Geom. 14, 1–6 (1979)
An, J.: Rigid geometric structures, isometric actions, and algebraic quotients. Geometriae Dedicata 157, 153–185 (2012)
Bader, U., Frances, C., Melnick, K.: An embedding theorem for automorphism groups of Cartan geometries. Geom. Funct. Anal. 19(2), 333–355 (2009)
Candel, A., Quiroga-Barranco, R.: Connections preserving actions are topologically engaging. Bol. Soc. Mat. Mex. 100, 123–155 (2001)
Candel, A., Quiroga-Barranco, R.: Gromov’s centralizer theorem. Geometriae Dedicata 100, 123–155 (2003)
Candel, A., Quiroga-Barranco, R.: Rigid and finite type geometric structures. Geometriae Dedicata 106, 123–143 (2004)
Candel, A., Quiroga-Barranco, R.: Parallelisms, prolongations of Lie algebras and rigid geometric structures. Manuscr. Math. 113(3), 335–350 (2004)
D’Ambra, G., Gromov, M.: Lectures in Transformations Groups: Geometry and Dynamics in Surveys in Differential Geometry (Cambridge, MA, 1990), pp. 19–111. Cambridge, Lehigh Univ. Bethlehem (1991)
Duistermaat, J.J., Kolk, J.A.: Lie Groups, Universitex. Springer, New York (1999)
Feres, R.: Dynamical Systems and Semisimple Groups in Tracts in Mathematics 126. Cambridge University Press, New York (1998)
Gromov, M.: Rigid Transformations Groups in Géométrie Différentielle, Paris 1986, pp. 65–139. Travaux en Cours, 33, Hermann, Paris (1988)
Nomizu, K.: On local and global existence of Killing vector fields. Ann. Math. 72, 105–120 (1960)
Rosales-Ortega, J.: The Gromov’s centralizer theorem for semisimple Lie group actions. Ph.D. thesis, CINVESTAV-IPN (2005)
Zimmer, R.J.: Ergodic Theory and Semi-simple Lie Groups. Birkhäuser, Boston (1984)
Zimmer, R.J.: On the automorphism group of a compact Lorentz manifold and other geometric manifolds. Invent. Math. 83, 411 (1986)
Zimmer, R.J.: Superrigidity, Ratner’s theorem and fundamental groups. Isr. J. Math. 74, 199–207 (1991)
Zimmer, R.J.: Automorphism groups and fundamental group of geometric manifold. Proc. Symposia Pure Math. 54, 693–710 (1993)
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Rosales-Ortega, J. The Gromov’s centralizer theorem for semisimple Lie group actions. Bol. Soc. Mat. Mex. 23, 825–845 (2017). https://doi.org/10.1007/s40590-015-0084-4
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DOI: https://doi.org/10.1007/s40590-015-0084-4