Address:
Charles University, Faculty of Mathematics and Physics, Sokolovská 83, Praha, Czech Republic
University of Bath, Department of Mathematical Sciences, Bath BA2 7AY, UK
E-mail: pucek.roland@gmail.com
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.
AMSclassification: primary 53A40; secondary 53B35.
Keywords: spinorial geometry, metrisability problem, equivalence problem, first BGG operator.
DOI: 10.5817/AM2017-5-325