Jaehyun Hong, Seoul National U., Korea

Complexifications of real symmetric spaces

Abstract:

An adapted complex structure of a complete Riemannian manifold is a complex structure on an open neighborhood of the zero section in its tangent bundle which is compatible with the Riemannian metric. For real symmetric spaces of compact type, the adapted complex structure exists on the whole tangent bundle. But usually it does not exist on the whole tangent bundle.

The maximal domain of the adapted complex structure of a real symmetric space of noncompact type has many interesting properties. We will review some of them and describe similarities with bounded symmetric domains.