Generalised Einstein equations and prescribed relations for the first Chern Weil form
type: Item
instance of: scholarly article
title: Generalised Einstein equations and prescribed relations for the first Chern Weil form
zbMATH Open document ID: 1054.32011
published in: Annals of Global Analysis and Geometry
publication date: 2004-08-20T00:00:00Z
review text: The author considers generalizations of the Einstein equation on a (closed) Kähler manifold \(V\) with a fixed Kähler form \(\omega\). To describe it, let \(\lambda\) be \(-1,0,1\) according to the curvature of the anticanonical bundle of \(V\) and \(\omega_x=\omega +\sqrt{-1}\partial \overline\partial x\) for a function \(x\) belonging to a Banach space of functions on \(V\) in which the test functions are dense. The equation discussed in the paper is \(\sqrt{-1}\text{Ric}(\omega_x)-\lambda\omega_x= \sqrt{-1}\partial\overline \partial((t-\lambda)x-sz)\), where \(z\) is a given function on \(V\) and \(t,s\) are real parameters. The main results of the paper (Theorems 1.1, 1.2) give sufficient conditions for the existence and unicity of solutions of certain regularity.
reviewed by: Liviu Ornea
Mathematics Subject Classification ID: 32J27
Mathematics Subject Classification ID: 32Q20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 2093681
zbMATH Keywords: Kähler-Einstein metric
zbMATH Keywords: Chern-Weil form
zbMATH Keywords: Ricci curvature
zbMATH Keywords: nonlinear elliptic equation
author: Daniel J. Pons
MaRDI profile type: Publication
full work available at URL: b:agag.0000018557.28153.ff
OpenAlex ID: W2011375978
DOI: 10.1023/B:AGAG.0000018557.28153.FF
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description: scientific article; zbMATH DE number 2093681