Subriemannian metrics and the metrizability of parabolic geometries

David M. J. Calderbank, Jan Slovak, Vladimir Soucek

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We present the linearized metrizability problem in the context of parabolic geometries and subriemannian geometry, generalizing the metrizability problem in projective geometry studied by R. Liouville in 1889. We give a general method for linearizability and a classification of all cases with irreducible defining distribution where this method applies. These tools lead to natural subriemannian metrics on generic distributions of interest in geometric control theory.
Original languageEnglish
Pages (from-to)1671–1702
Number of pages32
JournalJournal of Geometric Analysis
Issue number2
Early online date16 Nov 2019
Publication statusPublished - 1 Feb 2021

Bibliographical note

Funding Information:
The authors thank the Czech Grant Agency, Grant Nr. P201/12/G028, for financial support.

Publisher Copyright:
© 2019, Mathematica Josephina, Inc.


  • math.DG
  • 53B15, 53C17, 14M15, 17B10, 22E46, 53C15, 53C30, 58A32, 58J70, 93C10


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