Spin structures on real projective quadrics
This paper constructs the spin structures on the real quadric \(Qp,q\) compatible with the usual Riemannian metric and pseudo-Riemannian metric of signature \((p,q)\). If one lets the projective space \(RP^{p+q+1}\) be the equivalence classes of \((p+q+2)\)-tuples \((x_ 0,\dots,x_ p,\;y_ 0,\dots,y_ q)\) with \(\sum x^ 2_ i+\sum y^ 2_ i=1\), identifying \((x,y)\) with \((-x,-y)\), then the quadric \(Qp,q\) is the subset satisfying \(\sum x^ 2_ i-\sum y^ 2_ i=0\).
scientific article; zbMATH DE number 219770
scientific article