Subriemannian metrics and the metrizability of parabolic geometries

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

doi:10.1007/s12220-019-00320-1

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 language	English
Journal	Journal of Geometric Analysis
Early online date	16 Nov 2019
DOIs	https://doi.org/10.1007/s12220-019-00320-1
Publication status	E-pub ahead of print - 16 Nov 2019

Keywords

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

Cite this

Calderbank, D. M. J., Slovak, J., & Soucek, V. (2019). Subriemannian metrics and the metrizability of parabolic geometries. Journal of Geometric Analysis. https://doi.org/10.1007/s12220-019-00320-1

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AB - 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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Access to Document

10.1007/s12220-019-00320-1

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