On non-simply connected manifolds with non-trivial parallel spinors (Q1891976)

In this paper the author studies the possibilities of the full holonomy groups of locally irreducible but not necessarily complete Riemannian spin manifolds admitting a nontrivial parallel spinor (and the related notion of Killing spinors) and the dimension \(N\) of the space of parallel spinors. Four important theorems and one proposition as well as some corollaries are proved. A discussion of the results is given, particularly in relation to the use of parallel spinors in global supersymmetric transformations.