Jet-determination of symmetries of parabolic geometries

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Abstract

We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries—in particular torsion-free, parabolic contact, and several other classes.

Mathematics Subject Classification

Primary 58D19 Secondary 57S25 58K70 22F30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TromsøTromsøNorway
  2. 2.Fakultät für MathematikUniversität WienWienAustria
  3. 3.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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