Summary: On the characteristic torsion of gwistor space
October 24, 2010
We compute the characteristic torsion Tc of the G2-twistor space of an oriented
Riemannian 4-manifold with constant sectional curvature c and deduce the condition
under which Tc is c-parallel; this allows for the classification of the G2 characteristic
holonomy according to .
Key Words: metric connections, characteristic torsion, Einstein manifold, G2 struc-
MSC 2010: Primary: 53C10, 53C20, 53C25; Secondary: 53C28
The author acknowledges the support of Funda¸c~ao Ci^encia e Tecnologia, Portugal,
through Centro de Investiga¸c~ao em Matem´atica e Aplica¸c~oes da Universidade de ´Evora
(CIMA-U´E) and the sabbatical grant SFRH/BSAS/895/2009.
1.1 The purpose
It has now become clear that every oriented Riemannian 4-manifold M gives rise to a G2-
twistor space, as well as its celebrated twistor space. The former was first discovered in
[6, 7] and we shall start here by recalling how it is obtained. Often we abbreviate the name