On the curvature of homogeneous Kähler metrics of bounded domains
type: Item
instance of: scholarly article
title: On the curvature of homogeneous Kähler metrics of bounded domains
zbMATH Open document ID: 0699.53056
DOI: 10.1007/BF01790355
author: Laura Geatti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1989-01-01T00:00:00Z
review text: An n-dimensional Riemannian manifold is called a harmonic space if in a neighborhood of each point \(m_ 0\) in M, there exists a harmonic function f(m) depending only on the distance of m from \(m_ 0\) [\textit{H. S. Ruse}, \textit{A. G. Walker} and \textit{T. J. Willmore}, Harmonic spaces (1961; Zbl 0134.392)] and [\textit{A. L. Besse}, Manifolds all of whose geodesics are closed (1978; Zbl 0387.53010)]. It was shown by \textit{E. T. Copson} and \textit{H. S. Ruse} in [Proc. R. Soc. Edinb., Sect. A 60, 117- 133 (1940)], by \textit{A. Lichnerowicz} in [Bull. Soc. Math. Fr. 72, 146- 168 (1944; Zbl 0060.385)] and by \textit{A. J. Ledger} in [Ph. D. Thesis, Univ. Durham (1954)] that the curvature tensor of a harmonic space must satisfy an infinite sequence of conditions \(H_ k\). In the present paper, the author investigates the conditions \(H_ 1\) and \(H_ 2\) on the Riemannian manifolds obtained from a bounded domain D in \(C^ n\), endowed with a homogeneous Kähler metric.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 4147033
zbMATH Keywords: harmonic space
zbMATH Keywords: curvature tensor
zbMATH Keywords: Kähler metric
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01790355
OpenAlex ID: W2085152049
description: scientific article; zbMATH DE number 4147033