The spinor bundle of Riemannian products

Frank Klinker

paper

The spinor bundle of Riemannian products

arXiv:math/0212058

Abstract

In this note we compare the spinor bundle of a Riemannian manifold $(M = M_{1} \times ... \times M_{N}, g)$ with the spinor bundles of the Riemannian factors $(M_{i}, g_{i})$ . 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 $(M_{i}, g_{i})$ in an appropriate way.

7 pages (v2: added one reference)