The spinor bundle of Riemannian products
Frank Klinker
Abstract
In this note we compare the spinor bundle of a Riemannian manifold (M=M1×...× MN,g) with the spinor bundles of the Riemannian factors (Mi,gi). We show, that - without any holonomy conditions - the spinor bundle of (M,g) for a special class of metrics is isomorphic to a bundle obtained by tensoring the spinor bundles of (Mi,gi) in an appropriate way.
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