Geometry of geodesic spheres in a complex projective space

A geodesic sphere G(γ) of radius γ (0 < γ < π/√c ) of a complex projecive space CPn(c) is one of the most interesting objects in differential geometry.
This expository paper consists of two parts. In the first half, we study curve theory on G(γ) (see [4, 9]). In the latter half, we investigate G(γ) from the viewpoint of submanifold theory ([2, 11]).