The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry

Details The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry

2008-07-10

arxiv.org/abs/0807.1601v3

Mathematics

Differential Geometry

23pages

Scientific paper

In this paper, we first define the complexification of real analytic map between real analytic Koszul manifolds. As a special case, the extrinsic complexification of a real analytic pseudo-Riemannian submanifold is defined. Next we define an anti-Kaehler metric compatible with the adapted complex structure on the complexification of a real analytic pseudo-Riemannian manifold. The main purpose of this paper is to show that almost all orbits of some action on the complexification (equipped with the above anti-Kaehler metric) of a pseudo-Riemannian symmetric space are isoparametric.

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