Geometry on the variety of subspaces with positive definite form: geometry of the Grassmann spaces over generalized hyperbolic spaces (Q2044464)

Given a bilinear form \(\xi\) on a real vector space \(V\), consider those subspaces on which \(\xi\) restricts as a positive definite form. One can then define corresponding Grassmannians and spaces of (projective) pencils of those spaces. This paper proves results about definability (in the sense of first-order formulas) of these structures relative to each other. These generalise previously known results about Grassmannians on hyperbolic spaces.