Subriemannian Metrics and the Metrizability of Parabolic
Geometries

J 2021

Subriemannian Metrics and the Metrizability of Parabolic Geometries

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

Základní údaje

Originální název

Subriemannian Metrics and the Metrizability of Parabolic Geometries

Autoři

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

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.002

Kód RIV

RIV/00216224:14310/21:00118730

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1007/s12220-019-00320-1

UT WoS

000575577900001

EID Scopus

2-s2.0-85075486119

Klíčová slova anglicky

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

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 28. 4. 2022 08:52, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GBP201/12/G028, projekt VaV

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

Investor: Grantová agentura ČR, Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Citovat

CALDERBANK, David M. J.; Jan SLOVÁK a Vladimír SOUČEK. Subriemannian Metrics and the Metrizability of Parabolic Geometries. The Journal of Geometric Analysis. New York: Springer, 2021, roč. 31, č. 2, s. 1671-1702. ISSN 1050-6926. Dostupné z: https://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 = {https://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 a Vladimír SOUČEK. Subriemannian Metrics and the Metrizability of Parabolic Geometries. \textit{The Journal of Geometric Analysis}. New York: Springer, 2021, roč.~31, č.~2, s.~1671-1702. ISSN~1050-6926. Dostupné z: https://doi.org/10.1007/s12220-019-00320-1.

Přehled o publikaci