Subriemannian Metrics and the Metrizability of Parabolic
Geometries

J 2021

Subriemannian Metrics and the Metrizability of Parabolic Geometries

CALDERBANK, David M. J.; Jan SLOVÁK and Vladimír SOUČEK

Basic information

Original name

Subriemannian Metrics and the Metrizability of Parabolic Geometries

Authors

CALDERBANK, David M. J.; Jan SLOVÁK (203 Czech Republic, guarantor, belonging to the institution) and Vladimír SOUČEK

Edition

The Journal of Geometric Analysis, New York, Springer, 2021, 1050-6926

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 1.002

RIV identification code

RIV/00216224:14310/21:00118730

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s12220-019-00320-1

UT WoS

000575577900001

EID Scopus

2-s2.0-85075486119

Keywords in English

Bernstein-Gelfand-Gelfand resolution; Cartan geome;try; Overdetermined linear; Weyl connections PDE; Parabolic geometry; Projective metrizability; Subriemannian metrizability;

Abstract

In the original language

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.

Links

GBP201/12/G028, research and development project

Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Czech Science Foundation

Cite

CALDERBANK, David M. J.; Jan SLOVÁK and Vladimír SOUČEK. Subriemannian Metrics and the Metrizability of Parabolic Geometries. The Journal of Geometric Analysis. New York: Springer, 2021, vol. 31, No 2, p. 1671-1702. ISSN 1050-6926. Available from: https://dx.doi.org/10.1007/s12220-019-00320-1.

@article{1645757,
   author = {Calderbank, David M. J. and Slovák, Jan and Souček, Vladimír},
   article_location = {New York},
   article_number = {2},
   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;},
   language = {eng},
   issn = {1050-6926},
   journal = {The Journal of Geometric Analysis},
   title = {Subriemannian Metrics and the Metrizability of Parabolic Geometries},
   url = {https://link.springer.com/article/10.1007%2Fs12220-019-00320-1},
   volume = {31},
   year = {2021}
}

TY  - JOUR
ID  - 1645757
AU  - Calderbank, David M. J. - Slovák, Jan - Souček, Vladimír
PY  - 2021
TI  - Subriemannian Metrics and the Metrizability of Parabolic Geometries
JF  - The Journal of Geometric Analysis
VL  - 31
IS  - 2
SP  - 1671-1702
EP  - 1671-1702
PB  - Springer
SN  - 10506926
KW  - Bernstein-Gelfand-Gelfand resolution
KW  - Cartan geome;try
KW  - Overdetermined linear
KW  - Weyl connections PDE
KW  - Parabolic geometry
KW  - Projective metrizability
KW  - Subriemannian metrizability;
UR  - https://link.springer.com/article/10.1007%2Fs12220-019-00320-1
L2  - https://link.springer.com/article/10.1007%2Fs12220-019-00320-1
N2  - 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.
ER  -

CALDERBANK, David M. J.; Jan SLOVÁK and Vladimír SOUČEK. Subriemannian Metrics and the Metrizability of Parabolic Geometries. \textit{The Journal of Geometric Analysis}. New York: Springer, 2021, vol.~31, No~2, p.~1671-1702. ISSN~1050-6926. Available from: https://dx.doi.org/10.1007/s12220-019-00320-1.

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