The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin hypersurfaces

The main purpose of this paper is to investigate the quadraticity of slices (i.e., leaves of curvature foliations) of a non-degenerate equiaffine Dupin hypersurface, where an equiaffine Dupin hypersurface is the notion defined as the equiaffine geometrical version of a (not necessarily complete) Dupin hypersurface.