Spin structures and Killing spinors on lens spaces (Q1103234)

We determine the values of m and p for which a lens space \({\mathbb{Z}}_ p\setminus S^{2m-1}\) admits a spin structure. We prove that the only lens spaces (with dimension \(>3)\) admitting a maximal number of linearly independent Killing spinors are the real projective spaces \({\mathbb{P}}^{4k-1}({\mathbb{R}})\).