A Laplace integral on a Kähler manifold and Calabi's diastasis function

Abstract

In this paper we give a different proof of Engliš's result [J. Reine Angew. Math. 528 (2000) 1–39] about the asymptotic expansion of a Laplace integral on a real analytic Kähler manifold ( M , g ) by using the link between the metric g and the associated Calabi's diastasis function D. We also make explicit the connection between the coefficients of Engliš' expansion and Gray's invariants [Michigan Math. J. (1973) 329–344].