1. What is nilpotent structure on Riemannian manifold?

2. The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied.

3. Then-dimensional umbilical submanifolds in a Riemannian manifold of quasi constant curvature are discussed. Two theorems on the above submanifolds are obtained.

4. The relationship between the Riemannian geometric framework of Lagrange equation and the topology graph representation of classic mechanical systems is discussed.

5. The dynamic problem of constrained multibody systems in Riemannian configuration space is researched.

6. J . Cheeger, Comparison Theorems in Riemannian Geometry, North - Holland publishing company.

7. Positive curvature has been a frequent subject in Riemannian geometry.

8. Einstein manifold is a particular kind of Riemannian Manifold, it has good characters, its definition is weaker than Riemannian Manifold with constant sectional curvature.

9. Using the Riemannian geometry language, the modeling and control of general parallel robots are studied.

10. The b -boundary is the projection into a space-time of a natural boundary attached to a higher-dimensional Riemannian manifold.

11. To connect this point of view with the classical theory of surfaces, such an abstract surface is embedded into R 3 and endowed with the Riemannian metric given by the first fundamental form.

12. The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.

13. In this paper,[sentencedict.com/riemannian.html] the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal Riemannian symmetric spaces by computing the fundamental group.

14. Under a suitable condition, this paper gives an existence theorem for harmonic maps from surfaces to certain Riemannian manifolds in a large scale.

15. HCMU metric is a special kind of extremal metric on Riemannian surface with global rotational symmetric.

16. It can be excluded with data dependent way based on Riemannian geometry for improved SVM.

17. Through using the inertial matrix, we analyse the manipulation of robot by the Riemannian curvature.

18. As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.

19. A nonexistence theorem is established for F-harmonic map with finite F-energy from Euclidean space to any Riemannian manifold.

20. The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.

21. These results are in agreement with those obtained by general relativity expressed in Riemannian geometry and that from practical observations.

22. This paper discusses the discrete series of the L 2 integrable differential forms for noncompact Riemannian symmetric spaces.

23. He introduced an entirely new idea which cut the Gordian knot that had held up the Ricci-flow approach – -bearing on the central question of "collapsing" in Riemannian geometry.

24. In the end, the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric.

25. These results are in agreement with those obtained by general relativity expressed in Riemannian geometry a...