Invariant prolongation of overdetermined PDEs in projective,
conformal, and Grassmannian geometry

J 2012

Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry

ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG and Matthias HAMMERL

Basic information

Original name

Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry

Name in Czech

Invariiantní prodloužení přeurčených PDE v projektivní, konfomní a Grassmanovské geometryi

Authors

ŠILHAN, Josef (203 Czech Republic, guarantor, belonging to the institution), Vladimír SOUČEK (203 Czech Republic), Petr SOMBERG (203 Czech Republic) and Matthias HAMMERL (40 Austria)

Edition

Annals of Global Analysis and Geometry, Springer, 2012, 0232-704X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.887

RIV identification code

RIV/00216224:14310/12:00059641

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s10455-011-9306-9

UT WoS

000303345300007

Keywords (in Czech)

Parabolická geometrie - prodlužování invariantních PDEs - BGG sekvence - traktorová kovariantní derivace - projektivní geometrie - konformní geometrie - Grassmannovská geometrie

Keywords in English

Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry

Abstract

ORIG CZ

V originále

This is the second in a series of articles on a natural modification of the normal tractor connection on parabolic geometries, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in Hammerl et al. (preprint) and then compute the prolongation covariant derivatives for a number of interesting examples in projective, conformal, and Grassmannian geometries.

In Czech

Toto je druhý ze série článků o přirozené modifikaci normální traktorové konexe v parabolických geometriích, která přirozeně prodlužuje přeurčený systém invariantních diferenciálních rovnic na podkladové varietě. Nejprve shrneme obecnou proceduru nalezenou v Hammerl at al. a pak spočítáme prodlužovací kovariantní derivaci pro několik zajímavých příkladů v projektivní, konformní a Grassmannovské geometrii.

Links

MSM0021622409, plan (intention)

Name: Matematické struktury a jejich fyzikální aplikace

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications

Citovat

ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG and Matthias HAMMERL. Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry. Annals of Global Analysis and Geometry. Springer, 2012, vol. 42, No 1, p. 121-145. ISSN 0232-704X. Available from: https://dx.doi.org/10.1007/s10455-011-9306-9.

@article{978395,
   author = {Šilhan, Josef and Souček, Vladimír and Somberg, Petr and Hammerl, Matthias},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s10455-011-9306-9},
   keywords = {Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry},
   language = {eng},
   issn = {0232-704X},
   journal = {Annals of Global Analysis and Geometry},
   title = {Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry},
   url = {http://www.springerlink.com/content/4l90g13057177556/},
   volume = {42},
   year = {2012}
}

TY  - JOUR
ID  - 978395
AU  - Šilhan, Josef - Souček, Vladimír - Somberg, Petr - Hammerl, Matthias
PY  - 2012
TI  - Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry
JF  - Annals of Global Analysis and Geometry
VL  - 42
IS  - 1
SP  - 121-145
EP  - 121-145
PB  - Springer
SN  - 0232704X
KW  - Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry
UR  - http://www.springerlink.com/content/4l90g13057177556/
L2  - http://www.springerlink.com/content/4l90g13057177556/
N2  - This is the second in a series of articles on a natural modification of the normal tractor connection on parabolic geometries, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in Hammerl et al. (preprint) and then compute the prolongation covariant derivatives for a number of interesting examples in projective, conformal, and Grassmannian geometries.
ER  -

ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG and Matthias HAMMERL. Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry. \textit{Annals of Global Analysis and Geometry}. Springer, 2012, vol.~42, No~1, p.~121-145. ISSN~0232-704X. Available from: https://dx.doi.org/10.1007/s10455-011-9306-9.

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