  These are lecture notes on the rigidity of submanifolds of projective space
"resembling" compact Hermitian symmetric spaces in their homogeneous
embeddings. Recent results are surveyed, along with their classical
predecessors. The notes include an introduction to moving frames in projective
geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new
variant of the Hwang-Yamaguchi theorem.
