Almost c-spinorial geometry

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)325-334
Number of pages10
JournalArchivum Mathematicum
Volume53
Issue number5
DOIs
Publication statusPublished - 2017

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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