{\displaystyle {\mathrm {Spin} }(n).} Clifford bundle Clifford module bundle Orthonormal frame bundle Spin geometry Spinor Spinor representation Friedrich, Thomas (2000)...

tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to...

case of the Atiyah–Singer–Dirac operator acting on sections of a spinor bundle. For a spin manifold, M, the Atiyah–Singer–Dirac operator is locally defined...

a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in...

infinite rank vector bundle; this is the symplectic spinor construction due to Bertram Kostant. A section of the symplectic spinor bundle Q {\displaystyle...

differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine...

a spinor bundle. In fact, on a Spin manifold, every Clifford module is obtained by twisting the spinor bundle. The notion "Clifford module bundle" should...

being an integrability condition so that the Frobenius theorem applies. Spinor bundle All of these constructions are due to Ehresmann (1941-3). Attributed...

variety of Projective pure spinors, or simple spinor variety, of dimension m(m + 1)/2. (Another description of the pure spinor variety is as OGr + ⁡ ( m...

algebra on spinors. A spinor is said to be a pure spinor if it is annihilated by half of a set of a set of generators of the Clifford algebra. Spinors are sections...