Almost c-spinorial geometry

Roland Pucek

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)325-334
Number of pages10
JournalArchivum Mathematicum
Issue number5
Publication statusPublished - 2017


  • Equivalence problem
  • First BGG operator
  • Metrisability problem
  • Spinorial geometry

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Almost c-spinorial geometry'. Together they form a unique fingerprint.

Cite this