# Almost c-spinorial geometry

Archivum Mathematicum (2017)

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

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topPúček, 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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