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

Abstract

In this paper, we develop fundamentals of the dual theory of quadratic hyperband distributions H of m-dimensional line elements in a projective-metric space Kn (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.