Journal of the
Korean Mathematical Society JKMS

Most of domains people have studied are convex bounded projective (or affine) domains. Edith Soci\'{e}-M\'{e}thou [15] characterized ellipsoid in ${\mathbb R}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

Keywords: quadratic, projective domains, automorphism, ellipsoid, scaling sequence, unbounded domains

MSC numbers: 53A20