Dual affine connections on a quadratic hyperband distribution in a projective-metric space and their applications

In this paper, we develop fundamental of the dual theory of quadric hyperbandal distribution $H$ of $m$-dimensional line elements in a projective metric space $K_n$ ($m<n-1$). In particular, we show that, on a dual normalized distribution $H$, there are induced two dual affine connections and indicate some applications of these connections to the geometry of $m$-webs on $H$.