Fritz John necessary optimality condition on Riemannian manifolds;

Pseudo-Umbilical Submanifolds in a Locally Symmetric Conformally Flat Riemannian Manifold;

Intrinsic rigidity on minimal submanifolds in a Locally symmetric conformally flat Riemannian manifold;

Delaunay triangulation and Voronoi diagrams for Riemannian manifolds

The studies of differential manifolds and their applications are motivated to the active fields with applications of Riemanian manifolds and Sub-Riemannian manifolds in Control Theory,Dynamics Theory,Gauge Fields,etc.

Estimations of the moments of the hitting time by Brownian motions on general Riemannian manifolds are also obtained.

Nonlinear control systems on the riemann manifold;

In this article,taking smooth vector field on manilotd as state usctor field of dynamic system,we establishes differential dynamic systcm on the Riemann manifold and discuss the existenceand uuiqueness of solution of ynamic system,an effect of geometrical structure on structure stability and sinplified of dynamic system\

Let M and M′ be two Riemann manifolds.

Let N n+p p be a locally symmetric, complete and connected pseudo Riemannian manifold, whose sectional curvature K N satisties c 1≤K N≤c 2.

For a given covariant symmetric tensor field of order 2 on a pseudo Riemannian manifold,the author constructed a C ∞ locally orthonormal frame field such that with respect to the frame field the component matrix of the tensor field has of canonical form under some assumptions.

In this paper we study the geodesics in sub-Riemannian manifold (M,D,g) ,where M(?)R~3=R_x~2×R_t is a three dimentional smooth manifold , D is a two dimentional smooth horizontal distribution generated by vector fieldsinteger, and g is a positive definite metric defined on D .

In this paper, the geodesics in a class of sub-Riemannian manifolds-Carnot groups are studied.

An integral inequality for pseudo-umbilical space-like submanifolds in locally symmetric pseudo-Riemannian manifolds is presented,and the result from locally symmetric spaces is extended to pseudo-Riemannian manifolds.

In this paper,the pseudo-umbilical submanifolds with parallel mean curvature vector in pseudo-Riemannian manifold is discussed.

Let \$N\+\{n+p\}\-p\$ be an \$(n+p)\$-dimensional,complete and connected pseudo-Riemannian manifold,whose sectional curvature \$K\-N\$ satisfies \$a≤K\-N≤b\$.