2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65881In 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)Differential GeometryMathematical Physics15A66; 53C27text