Subriemannian metrics and the metrizability of parabolic geometries

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

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Abstract

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
JournalJournal of Geometric Analysis
Early online date16 Nov 2019
DOIs
Publication statusE-pub ahead of print - 16 Nov 2019

Keywords

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

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