
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.
pseudo-Kähler metric, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Differential geometry of homogeneous manifolds, generalized flag manifolds, Global differential geometry of Hermitian and Kählerian manifolds, \(T\)-root system
pseudo-Kähler metric, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Differential geometry of homogeneous manifolds, generalized flag manifolds, Global differential geometry of Hermitian and Kählerian manifolds, \(T\)-root system
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 4 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
