Parallel spinors and basic holonomy in pseudo-Hermitian geometry
The relationship between parallel sections in vector bundles and holonomy with respect to the Webster-Tanaka connection of pseudo-Hermitian geometry is studied. This is an interesting question in particular in the Cauchy-Riemann geometry setting. This connection can be regarded as a metric one with torsion. However, the behavior of its pseudo-Hermitian holonomy group is not completely natural and that is why the author endeavors in this paper to introduce an adjusted connection, called by the basic connection of pseudo-Hermitian geometry with corresponding basic holonomy group. Basic holonomy groups are suitable to describe pseudo-Einstein spaces and to consider the existence of parallel spinor fields. As one of the main results of this work, it is shown that the basic holonomy algebra of any pseudo-Einsten space is reduced to the special unitary algebra.
scientific article; zbMATH DE number 7037383
scientific article