Abstract
A pseudo-Kähler manifold is a natural generalization of a Kähler manifold. It is well-known that any generalized flag manifold has pseudo-Kähler metrics. Moreover, there exists a -root system corresponding to a generalized flag manifold. In this paper, we investigate the signatures of invariant pseudo-Kähler metrics on a generalized flag manifold of which the -root system becomes one of the irreducible reduced root systems (in general, a -root system is not an irreducible reduced root system).
Funding Statement
The author is supported by JSPS KAKENHI Grant number JP16K05131.
Acknowledgement
The author would like to express his deep appreciation to Professor Yusuke Sakane for valuable advices and encouragements.
Citation
Takumi Yamada. "Remarks on the signatures of invariant pseudo-Kähler metrics on generalized flag manifolds." Hiroshima Math. J. 52 (2) 139 - 152, July 2022. https://doi.org/10.32917/h2016091
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