| 1. | A compact minimal submanifold of sasakian space form
空间形式中的紧致极小子流形 |
| 2. | The global properties of minimal submanifold and k hler complex submanifold
复子流形的整体性质 |
| 3. | Complex analytic submanifold
复解析子流形 |
| 4. | In this paper , we studied the co - dimension decreasing of submanifold . we point out that on certain condition , the co - dime nsion can be reduced to 1
本文研究了常曲率空间子流形余维数减少的问题,说明了在一定条件下,余维数可以减少到1 |
| 5. | In the third second , we study a closed oriented submanifold with parallel mean curvature vector field in a sphere . let s = s - nh2 . we fist obtain a pinching theorem on 5
第三节中研究了欧氏球面中具有常平均曲率向量子流形，获得两个结果，其中一个结果推广了h |
| 6. | While the new components having the same numbers with these original physical vectors are introduced and the new components are combined with those original physical components to form a new symplectic space , the ray problem of wave propagation in geometrical optics is converted into the problem of lagrange submanifold in the symplectic space
通过引入波向量(慢度向量) ，将物理空间中几何光学的射线问题转化为辛空间中的lagrange子流形(超曲面)问题。 |
| 7. | The compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold are studied , and obtain the following intrinsic rigidity theorem . i . e . if m be a compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold n ( superscript n + p )
摘要研究了局部对称共形平坦黎曼流形的紧致极小子流形，即设m是局部对称共形平坦黎曼流形的n维紧致极小子流形，得到了这种子流形的若干内蕴刚性积分不等式，给出了流形全测地的限制条件。 |
| 8. | Then a probability distribution of the states at the equilibrium corresponding a self - assembly model . all the possible can form a manifold called s , and the probability distribution of the states self - assembly system reached form a submanifold of 5 " , called a . so the difference of two self - assembly model is the division of two probability distribution at the manifold
这里，我们利用信息几何的知识给出了dna自装配的一个形式化模型，以分子两两构成的组合的个数为分量组成的向量表示自装配过程中的一个状态，那么，当每自装配系统达到平衡时，就有一个关于这些状态的一个概率分布，所有可能的概率分布形成了一个微分流形s 。 |
| 9. | Since the cause of caustics phenomena is that the tangent plane of lagrange submanifold in caustic fields is perpendicular to the original physical space , we solve the high frequency asymptotic problem in a new mixed space by changing the projecting direction , then we get the high frequency asymptotic solutions of wave equations efficiently near and on the caustics
由于出现焦散现象的原因在于lagrange子流形在该处的切平面与物理空间垂直，通过转换适当的投影方向，然后将这个投影方向上得到的高频近似解再变换回到原来的物理空间中，得到了在焦散附近适用的高频近似解。 |
