Invariant pseudo-Kähler metrics on generalized flag manifolds
type: Item
instance of: scholarly article
title: Invariant pseudo-Kähler metrics on generalized flag manifolds
zbMATH Open document ID: 1305.53054
author: Takumi Yamada
published in: Differential Geometry and its Applications
publication date: 2014-10-06T00:00:00Z
review text: A pseudo-Riemannian manifold \((M,g)\) with a complex structure \(J\) is called a \textit{pseudo-Kähler manifold} if \(g\) is a pseudo-Hermitian metric and the fundamental \(2\)-form \(\omega _{g}\) is closed. Hence, a pseudo-Kähler manifold is one of the natural generalizations of a Kähler manifold. Such a pseudo-Riemannian metric \(g\) is called \textit{pseudo-Kähler metric} and the fundamental \(2\)-form \(\omega _{g}\) \textit{pseudo-Kähler structure}. In this interesting paper, the author considers signatures of invariant pseudo-Kähler metrics on generalized flag manifolds from the viewpoint of \(T\)-root systems. By a result of Maschler, to investigate the signatures of the integral pseudo-Kähler metrics of a generalized flag manifold, it is sufficient to investigate the signatures of the invariant pseudo-Kähler metrics. By investigating patterns of signatures of invariant pseudo-Kähler metrics on a generalized flag manifold, the author gets that two invariant complex structures \(J\) and \(J^{\prime }\) on a generalized flag manifold are either diffeomorphic or non-diffeomorphic.
reviewed by: Andreea Olteanu
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 6351463
zbMATH Keywords: pseudo-Kähler metric
zbMATH Keywords: generalized flag manifolds
zbMATH Keywords: \(T\)-root system
MaRDI profile type: Publication
full work available at URL: j.difgeo.2014.07.003
OpenAlex ID: W2048320039
Wikidata QID: Q115356187
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DOI: 10.1016/J.DIFGEO.2014.07.003
description: scientific article; zbMATH DE number 6351463