Some critical almost Hermitian structures
type: Item
instance of: scholarly article
title: Some critical almost Hermitian structures
zbMATH Open document ID: 1262.53027
author: Jeonghyeong Park
author: Jungchan Lee
author: Kouei Sekigawa
published in: Results in Mathematics
publication date: 2013-02-08T00:00:00Z
review text: Let \(M\) be a compact manifold of even dimension and \(\mathcal{AH}(M)\) the Frechet space of all almost Hermitian structures on \(M\). For a real number \(c>0\), let \(\mathcal{AH}_c(M)\) be the subset of such structures with volume \(c\). For \((\lambda , \mu )\in \mathbb R^2\setminus \{(0, 0)\}\) the functional \(\mathcal{F}_{\lambda , \mu }(J, g)=\int _M(\lambda \tau +\mu \tau ^\ast)dv_g\) is very important where \(\tau \) and \(\tau ^\ast\) are the scalar curvature and \(\ast\)-scalar curvature of \((J, g)\) respectively. The present paper is devoted to the study of the critical points of this functional on the subspaces of \(\mathcal{AH}(M)\) and \(\mathcal{AH}_c(M)\) provided by Hermitian, almost Kähler and nearly Kähler structures respectively. Some very interesting examples are discussed.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 58E11
zbMATH DE Number: 6135230
zbMATH Keywords: critical almost Hermitian structure
zbMATH Keywords: Einstein-Hilbert functional
MaRDI profile type: Publication
full work available at URL: s00025-011-0143-8
OpenAlex ID: W2016864122
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DOI: 10.1007/S00025-011-0143-8
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description: scientific article; zbMATH DE number 6135230