A Laplace integral on a Kähler manifold and Calabi's diastasis function
type: Item
instance of: scholarly article
title: A Laplace integral on a Kähler manifold and Calabi's diastasis function
zbMATH Open document ID: 1079.53104
author: Andrea Loi
published in: Differential Geometry and its Applications
publication date: 2005-08-05T00:00:00Z
review text: If \(M\) is a complex manifold endowed with a real analytic Kähler metric \(g\), and \(\alpha>1\), the Laplace integral of a smooth function \(f\) is defined by \[ L_\alpha(f)=\int_U f(y)\exp\bigl(-\alpha D(\cdot,y)\bigr)\omega^n(y)/n!, \] where \(\omega\) is the Kähler form of \(g\) and \(D\) is Calabi's diastasis function, defined on a suitable open subset \(U\times U\) of \(M\times M\). In this paper the author, using techniques due to \textit{M. Cahen, S. Gutt} and \textit{J. Rawnsley} [Trans. Am. Math. Soc. 337, No. 1, 73--98 (1993; Zbl 0788.53062)] generalizes results of \textit{M. Engliš} [J. Funct. Anal. 177, No. 2, 257--281 (2000; Zbl 0969.32003)] on the asymptotic expansion of \(L_\alpha(f)\) as \(\alpha\) goes to infinity.
reviewed by: Marco Abate
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 2192809
zbMATH Keywords: Kähler metric
zbMATH Keywords: diastasis
Wikidata QID: Q115357968
MaRDI profile type: Publication
full work available at URL: j.difgeo.2005.03.005
OpenAlex ID: W1988796260
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DOI: 10.1016/J.DIFGEO.2005.03.005
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description: scientific article