Almost c-spinorial geometry

Roland Pucek

doi:10.5817/AM2017-5-325

Almost c-spinorial geometry

Roland Pucek

Department of Mathematical Sciences

Charles University in Prague

Research output: Contribution to journal › Article › peer-review

Abstract

Almost c-spinorial geometry arises as an interesting example of the metrisability problem for parabolic geometries. It is a complex analogue of real spinorial geometry. In this paper, we first define the type of parabolic geometry in question, then we discuss its underlying geometry and its homogeneous model. We compute irreducible components of the harmonic curvature and discuss the conditions for regularity. In the second part of the paper, we describe the linearisation of the metrisability problem for Hermitian and skew-Hermitian metrics, state the corresponding first BGG equations and present explicit formulae for their solutions on the homogeneous model.

Original language	English
Pages (from-to)	325-334
Number of pages	10
Journal	Archivum Mathematicum
Volume	53
Issue number	5
DOIs	https://doi.org/10.5817/AM2017-5-325
Publication status	Published - 2017

Funding

Acknowledgement. The author would like to thank Vladimír Souček for helpful discussions. This research was supported by the institutional grant of the Charles University SVV 260456 and by the grant GACR 17-01171S.

Keywords

Equivalence problem
First BGG operator
Metrisability problem
Spinorial geometry

ASJC Scopus subject areas

General Mathematics

Access to Document

10.5817/AM2017-5-325

Cite this

@article{f5044ae428f14e1681fa1b3ac0a3f224,

title = "Almost c-spinorial geometry",

abstract = "Almost c-spinorial geometry arises as an interesting example of the metrisability problem for parabolic geometries. It is a complex analogue of real spinorial geometry. In this paper, we first define the type of parabolic geometry in question, then we discuss its underlying geometry and its homogeneous model. We compute irreducible components of the harmonic curvature and discuss the conditions for regularity. In the second part of the paper, we describe the linearisation of the metrisability problem for Hermitian and skew-Hermitian metrics, state the corresponding first BGG equations and present explicit formulae for their solutions on the homogeneous model.",

keywords = "Equivalence problem, First BGG operator, Metrisability problem, Spinorial geometry",

author = "Roland Pucek",

year = "2017",

doi = "10.5817/AM2017-5-325",

language = "English",

volume = "53",

pages = "325--334",

journal = "Archivum Mathematicum",

issn = "0044-8753",

publisher = "Masarykova Universita",

number = "5",

}

TY - JOUR

T1 - Almost c-spinorial geometry

AU - Pucek, Roland

PY - 2017

Y1 - 2017

N2 - Almost c-spinorial geometry arises as an interesting example of the metrisability problem for parabolic geometries. It is a complex analogue of real spinorial geometry. In this paper, we first define the type of parabolic geometry in question, then we discuss its underlying geometry and its homogeneous model. We compute irreducible components of the harmonic curvature and discuss the conditions for regularity. In the second part of the paper, we describe the linearisation of the metrisability problem for Hermitian and skew-Hermitian metrics, state the corresponding first BGG equations and present explicit formulae for their solutions on the homogeneous model.

AB - Almost c-spinorial geometry arises as an interesting example of the metrisability problem for parabolic geometries. It is a complex analogue of real spinorial geometry. In this paper, we first define the type of parabolic geometry in question, then we discuss its underlying geometry and its homogeneous model. We compute irreducible components of the harmonic curvature and discuss the conditions for regularity. In the second part of the paper, we describe the linearisation of the metrisability problem for Hermitian and skew-Hermitian metrics, state the corresponding first BGG equations and present explicit formulae for their solutions on the homogeneous model.

KW - Equivalence problem

KW - First BGG operator

KW - Metrisability problem

KW - Spinorial geometry

UR - http://www.scopus.com/inward/record.url?scp=85040723135&partnerID=8YFLogxK

U2 - 10.5817/AM2017-5-325

DO - 10.5817/AM2017-5-325

M3 - Article

AN - SCOPUS:85040723135

SN - 0044-8753

VL - 53

SP - 325

EP - 334

JO - Archivum Mathematicum

JF - Archivum Mathematicum

IS - 5

ER -

Almost c-spinorial geometry

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this