The spinor bundle of Riemannian products

Details The spinor bundle of Riemannian products The spinor bundle of Riemannian products

2002-12-04

arxiv.org/abs/math/0212058v2

Mathematics

Differential Geometry

7 pages (v2: added one reference)

Scientific paper

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.

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