Geodesic
Almost c-spinorial geometry
Archivum mathematicum, Tome 53 (2017) no. 5, pp. 325-334 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2017-5-325
Classification : 53A40, 53B35
Keywords: spinorial geometry; metrisability problem; equivalence problem; first BGG operator 
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Púček, Roland. Almost c-spinorial geometry. Archivum mathematicum, Tome 53 (2017) no. 5, pp. 325-334. doi: 10.5817/AM2017-5-325

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