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1.
本文讨论了黎曼流形上的射影半对称联络,即与Levi-Civita联络射影等价的半对称联络的一些性质,得到了黎曼流形射影平坦的一个充要条件,以及一些与黎曼流形上的射影变换有关的结果。  相似文献   

2.
局部对称共形平坦黎曼流形中的紧致子流形   总被引:6,自引:0,他引:6  
本文讨论局部对称共形平坦黎曼流形中紧子流形问题.改进了[1]的结果并将[2]中关于球面子流形的一个结果推广到局部对称共形平坦黎曼流形子流形.  相似文献   

3.
本文研究了Berwald流形之间的射影对应.利用Berwald流形上Weyl射影曲率张量的射影不变性,证明了当n>2时,与射影平坦的Berwald流形射影对应的黎曼流形M~n是常曲率流形,从而推广了Beltrami定理.  相似文献   

4.
该文讨论了某一类特殊流形的形状问题,即当某些紧的黎曼流形上存在一个非平凡的共形向量场且数量曲率为常数时,研究在什么情况下该流形等距于欧式空间中的球面.另外还研究当黎曼流形的数量曲率是非常数时相应的若干刚性定理.  相似文献   

5.
如果一个Yang-Mills场(规范群为任意李群)的场强的所有规范导数均为0,则称这个场为平行的Yang-Mills场。平行规范场是微分几何中对称空间的推广,它是Yang-Mills方程的特解。 本文的主要结果是下列两个定理: 定理1 容有非平凡的平行Yang-Mills场的四维黎曼空间必须是Khler流形或半对称空间,这里半对称流形是满足的黎曼流形,其中分别是曲率张量的自对偶部份及反自对偶部份,而“;”表示共变导数。 定理2 半对称空间如果不是对称空间,则必为Khler-Einstein空间或共形半平坦Einstein空间。这里共形半平坦是指Weyl张量的反自对偶部份或自对偶部份为0。 在附录中作者给出了二维黎曼流形上Yang-Mills方程的所有的整体解。  相似文献   

6.
本文首先将常曲率黎曼流形中B.Y.Chen和M.Okumura关于数量曲率和截面曲率关系间的一个著名不等式推广到环绕空间是局部对称共形平坦黎曼流形的情形.作为应用,较简捷地将M.Okumura在[2],[3]中的结果推广到这种环绕空间中法联络是平坦的子流形上去.  相似文献   

7.
蒋经农  程新跃 《数学杂志》2012,32(4):621-628
本文研究了反正切Finsler度量F=α+εβ+βarctan(β/α)与Randers度量F=α+β射影等价,这里α和α表示流形上的两个黎曼度量,β和β表示流形上的两个非零的1-形式.利用射影等价具有相同的Douglas曲率的性质,获得了这两类度量射影等价的充要条件.  相似文献   

8.
如果一个Yang-Mills场(规范群为任意李群)的场强的所有规范导数均为0,则称这个场为平行的Yang-Mills场.平行规范场是微分几何中对称空间的推广,它是Yang-Mills方程的特解. 本文的主要结果是下列两个定理: 定理1 容有非平凡的平行Yang-Mills场的四维黎曼空间必须是Kahler流形或半对称空间.这里半对称流形是满足 \[R_{ijkl}^ - = 0\](或\[R_{ijkl}^ + = 0\]) 的黎曼流形,其中\[R_{ijkl}^ \pm \]分别是曲率张量的自对偶部份及反自对偶部份,而":"表示共变 导数. 定理2 半对称空间如果不是对称空向,则必为Kahler-Einstein空间或共形半平坦Einstein空间.这里共形半平坦是指Weyl张量的反自对偶部份或自对偶部份为0.在附录中作者给出了二维黎曼流形上Yang-Mills方程的所有的整体解.  相似文献   

9.
本文研究了复射影空间中具有平行平均曲率向量的黎曼叶状结构(F).利用Nalcagawa 和Takagi的计算散度的方法,得到了复射影窄问中具有平行平均曲率向量的黎曼叶状结构(F)上向量场的散度,证明了其上的一个整体Pinching定理,从而将复射影空间中任何具有极小法平面场的调和叶的仵质推广到复射影窄间中具有平行平均曲率向量的黎曼叶状结构(F)上.  相似文献   

10.
不动点集为(■P(2r_i+1))■(■S~nj)的对合的流形   总被引:3,自引:1,他引:2  
本文讨论了不动点集F为任意多个奇维实数(复数、或者四元数)射影空间与球面不交并的闭流形M上对合T的流形(M,T),给出了这样的流形不协边的充要条件.  相似文献   

11.
The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4‐manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.  相似文献   

12.
The relation between Wild Topology, Hyperbolic Geometry and Fusion Algebra on the one side and the charge and coupling constants of the standard model and quantum gravity on the other is examined.

The close connection found between theory and the Topological theory of four manifolds as well as the theory of fundamental groups is elucidated using various classical theories and recent results due to Antoine, Wada, Alexander, Klein, Kummer, Freedman, Kaufmann, Witten, Jones and Connes.  相似文献   


13.
We construct invariants of four-dimensional piecewise linear manifolds, represented as simplicial complexes, with respect to moves that transform a cluster of three 4-simplices having a common two-dimensional face to a different cluster of the same type and having the same boundary. Our construction is based on using Euclidean geometric quantities.  相似文献   

14.
Annals of Global Analysis and Geometry - We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds...  相似文献   

15.
The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically Euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new context. Among these applications, we will show some rigidity results for asymptotically Euclidean Ricci-solitons and Codazzi-solitons. Also, we will present an almost-Schur type inequality valid in this non-compact setting which does not need restrictions on the Ricci curvature. Finally, we will show how some rigidity results related with static potentials also follow from these type of conservation principles.  相似文献   

16.
莫小欢 《数学进展》2005,34(3):257-268
本文回顾了近年来Finsler几何的进展.特别,我们描述了Finsler流形上几何不变量所满足的基本方程及其应用,并提出了相关的未解决的问题。  相似文献   

17.
We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces.  相似文献   

18.
We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces.  相似文献   

19.
Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12--16], we study the set of their singularities and for a particularclass of manifolds develop an extragradient-type algorithm convergent to singularities of such vector fields. In particular, our method can be used forsolving nonlinear constrained optimization problems in Euclidean space, with a convex objective function and the constraint set a constant curvature Hadamard manifold. Our paper shows how tools of convex analysis on Riemannian manifolds can be used to solve some nonconvex constrained problem in a Euclidean space.O.P. Ferreira- was supported in part by CAPES, FUNAPE (UFG) and (CNPq).S.Z. Németh- was supported in part by grant No.T029572 of the National Research Foundation of Hungary.  相似文献   

20.
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