  Every compact symmetric space $M$ admits a dual noncompact symmetric space
$\check{M}$. When $M$ is a generalized Grassmannian, we can view $\check{M}$ as
a open submanifold of it consisting of space-like subspaces \cite{HL}.
Motivated from this, we study the embeddings from noncompact symmetric spaces
to their compact duals, including space-like embedding for generalized
Grassmannians, Borel embedding for Hermitian symmetric spaces and the
generalized embedding for symmetric R-spaces. We will compare these embeddings
and describe their images using cut loci.
