Quadratic sets of a 3-dimensional locally projective regular planar space (Q1772526)

Let \((\mathcal S, \mathcal L, \mathcal P)\) be a 3-dimensional locally projective planar space in which all lines have the same length. A quadratic set of \(\mathcal S\) is defined exactly as in the case of projective spaces. The authors show that nondegenerate quadratic sets only exist in projective and affine spaces.