Publication details

Subriemannian Metrics and the Metrizability of Parabolic Geometries

Authors

CALDERBANK David M. J. SLOVÁK Jan SOUČEK Vladimír

Year of publication 2021
Type Article in Periodical
Magazine / Source The Journal of Geometric Analysis
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007%2Fs12220-019-00320-1
Doi http://dx.doi.org/10.1007/s12220-019-00320-1
Keywords Bernstein-Gelfand-Gelfand resolution; Cartan geome;try; Overdetermined linear; Weyl connections PDE; Parabolic geometry; Projective metrizability; Subriemannian metrizability;
Description 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.
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