Considering a projectively invariant metric on a strongly convex bounded domain, we study the asymptotic expansion of the scalar curvature with respect to the distance function, and use the Fubini–Pick invariant to describe the second term in the expansion. In particular for the two-dimensional convex domain, we also show that the third term in the expansion is zero.
This is a preview of subscription content, log in to check access
Jian, H., Wang, X.J.: Bernstein theorem and regularity for a class of Monge–Ampre equations. J. Diff. Geom. 93(3), 79–87 (2013)Google Scholar
Li, A.M., Simon, U., Zhao, G.: Global Affine Differetial Geometry of Hypersurfaces. Walter de Gruyter, Berlin (1993)CrossRefGoogle Scholar
Sasaki, T.: On the green function of a complete Riemannian or Kahler manifold with asymptotically negative constant curvature and applications. Adv. Stud. Pure Math. 3, 387–421 (1984)MATHGoogle Scholar