Almost c-spinorial geometry

Roland Púček

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 5, page 325-334
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Púček, Roland. "Almost c-spinorial geometry." Archivum Mathematicum 053.5 (2017): 325-334. <http://eudml.org/doc/294235>.

@article{Púček2017,
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.},
author = {Púček, Roland},
journal = {Archivum Mathematicum},
keywords = {spinorial geometry; metrisability problem; equivalence problem; first BGG operator},
language = {eng},
number = {5},
pages = {325-334},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Almost c-spinorial geometry},
url = {http://eudml.org/doc/294235},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Púček, Roland
TI - Almost c-spinorial geometry
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 5
SP - 325
EP - 334
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.
LA - eng
KW - spinorial geometry; metrisability problem; equivalence problem; first BGG operator
UR - http://eudml.org/doc/294235
ER -

References

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  9. Hammerl, M., Somberg, P., Souček, V., Šilhan, J., 10.4171/JEMS/349, J. Eur. Math. Soc. (JEMS) 14 (6) (2012), 1859–1883. (2012) Zbl1264.58029MR2984590DOI10.4171/JEMS/349
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