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- W4309683744 abstract "In this paper, we first define the complexification of a real analytic map between real analytic Koszul manifolds and show that the complexified map is the holomorphic extension of the original map. Next we define an anti-Kaehler metric compatible with the adapted complex structure on the complexification of a real analytic pseudo-Riemannian manifold. In particular, for a pseudo-Riemannian homogeneous space, we define another complexification and a (complete) anti-Kaehler metric on the complexification. One of main purposes of this paper is to find the interesting relation between these two complexifications (equipped with the anti-Kaehler metrics) of a pseudo-Riemannian homogeneous space. Another of main purposes of this paper is to show that almost all principal orbits of some isometric action on the first complexification (equipped with the anti-Kaehler metric) of a semi-simple pseudo-Riemannian symmetric space are curvature-adapted isoparametric submanifolds with flat section in the sense of this paper." @default.
- W4309683744 created "2022-11-29" @default.
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- W4309683744 date "2008-07-10" @default.
- W4309683744 modified "2023-10-01" @default.
- W4309683744 title "The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry" @default.
- W4309683744 doi "https://doi.org/10.48550/arxiv.0807.1601" @default.
- W4309683744 hasPublicationYear "2008" @default.
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