In this paper,we mainly discussed surfaces with one constant principal curvature in H3(-1),and then the realations between this constant principal curvature and the other one were found.

Let Nn+p be an n+p-dimensional locally symmetric complete quasi-constant curvature Riemannian manifold and Mn be an n-dimensional compact sub-manifold in Mn+p with paralleled mean curvature vector.

This paper presents a necessary and sufficient condition that the recurrent hypersurface M in a Riemannian space with quasi-constant curvature is locally symmetric,and shows that the complete irreducible birecurrent hypersurface M in a Riemannian space with quasi-constant curvature is recurrent if the generating element of N is a normal vector field or pungent vector field of M.

We generalize the two theorems of submanifolds in constant curvature manifolds to the external sphere mani-folds in quasi-constant curvature.

The authors study the property of a class of(α,β)-metrics F in which β is parallel with respect to Riemann metric α and Riemann metric α is of constant curvature,and it is obtained that F is flat-parallel metric or conformally related to Riemann metric α.

In the present paper, the authors first study Finsler spaces satisfying L_ :0+K(x, y)F2C=0, show that it must be of constant curvature, and obtain some interesting conclusions.

The purpose of this paper is to give some conditions which a Finsler space of constant curvature remains to be a Finsler space of constant curvature by a geodesic mapping of Finsler space.

Based on the idea of integrable system,taking advantage of matrix model for 3-dimensional Minkowski space L 3,the integrability and curved suface deformation of negative curvity in L 3 were studied.