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
Pages (from-to)	1671–1702
Number of pages	32
Journal	Journal of Geometric Analysis
Volume	31
Issue number	2
Early online date	16 Nov 2019
DOIs	https://doi.org/10.1007/s12220-019-00320-1
Publication status	Published - 1 Feb 2021

Keywords

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

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10.1007/s12220-019-00320-1

1803.10482v1.PDF
This is a post-peer-review, pre-copyedit version of an article published in The Journal of Geometric Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s12220-019-00320-1
Accepted author manuscript, 362 KB

David Calderbank
- D.M.J.Calderbank@bath.ac.uk
- Department of Mathematical Sciences - Professor
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching

Cite this

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title = "Subriemannian metrics and the metrizability of parabolic geometries",

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. ",

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AU - Soucek, Vladimir

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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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JO - Journal of Geometric Analysis

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ER -

Subriemannian metrics and the metrizability of parabolic geometries

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David Calderbank

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