The Riemannian metric of perspective in stereo graphic projection is introduced and a property of the continual cut vector field on the spherical surface is discussed.

We deduce the Riemannian metric on complex projective space from Riemannian submersion π:S2n+1→CPn,get its volume element We also prove that one type totally real submanifolds of CPn is none but ndimensional sphere Sn.

In this paper, we study some conditions and properties for an important class of randers metrics in forms of F(y)=(β(y)~2+(1-|β|~2)α(y)~2)~(1/2)-β(y)/1-|β|~2 to be pointwiseprojective toα,whereα(y)=(α_(ij)(x)y~iy~j)~(1/2) is a Riemannian metric on ann-dimensional manifold M andβ(y)=b_i(x)y~i is a 1-form on M.

It is well-known that there is a unique vertex on rotating parabolic surface in three-dimensional Euclidiean space,the paper generalizes the concept of vertex to a complete noncompact Riemannian manifold with nonnegative curvature.

The paper discusses the structure of the soul in a complete noncompact Riemannian manifold M with nonnegative curvature,and proves that if the soul of the manifold is unique,then the soul actually degenerates to a pole.

The parallel properties of the rays in a complete noncompact Riemannian manifoldM were discussed in this paper, It is proved that the Busemann functions corresponding to any given two parallel rays are just the same as each other in the sense of H.