在线词典

In differential geometry, given a spin structure on a n-dimensional Riemannian manifold (M, g),\, one defines the spinor bundle to be the complex vector bundle \pi_{\mathbf S}\colon{\mathbf S}\to M\, associated to the corresponding principal bundle \pi_{\mathbf P}\colon{\mathbf P}\to M\, of spin frames over M and the spin representation of its structure group {\mathrm {Spin}}(n)\, on the space of spinors \Delta_n.\,.