Statistical structures arising in null submanifolds

Abstract

We show a link between affine differential geometry and null submanifolds in a semi-Riemannian manifold via statistical structures. Once a rigging for a null submanifold is fixed, we can construct a semi-Riemannian metric on it. This metric and the induced connection constitute a statistical structure on the null submanifold in some cases. We study the statistical structures arising in this way. We also construct statistical structures on a null hypersurface in the Lorentz–Minkowski space using the null second fundamental form. This extends the classical construction to the null case.