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旋转向量场中闭轨线的方程 总被引:1,自引:0,他引:1
<正> G.F.D.Duff于1953年首次展开了旋转向量场的理论.后来G.Seifert改进了Duff的工作.本文主要在于建立旋转向量场中闭轨线的方程,并初步用它来计算含小参数的范德坡方程的极限环,这种方法较简便,且对旋转向量场中的合小参数的不少方程同样有效.我们采用 Seifert 关于旋转向量场的定义和术语.考察方程组 相似文献
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利用中心投影的思想证明了一类n+1次平面拟齐次向量场的几何性质仅依赖于它的诱导向量场.并根据其诱导向量场的性质证明了该向量场有10种不同拓扑结构的扇形不变区域,进而讨论了其全局拓扑结构,得到了该向量场当n为偶数时有13种不同的全局拓扑等价类,当n为奇数时有12种不同的全局拓扑等价类. 相似文献
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利用中心投影变换的思想证明一类平面三次拟齐次向量场的几何性质依赖于它的切向量场和诱导向量场.讨论了该系统的拓扑结构,并进行了分类;证明了该系统具有25类不同类的拓扑结构相图. 相似文献
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阿布迪夏克尔·吐力拜克 《数学的实践与认识》2015,(1):266-270
利用正则型方面的有关理论,讨论了平面向量场在双曲奇点附近的光滑线性化问题,对几类平面向量场给出了可以线性化的条件. 相似文献
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《Indagationes Mathematicae》2019,30(4):542-552
In this paper, we study the impact of geodesic vector fields (vector fields whose trajectories are geodesics) on the geometry of a Riemannian manifold. Since, Killing vector fields of constant lengths on a Riemannian manifold are geodesic vector fields, leads to the question of finding sufficient conditions for a geodesic vector field to be Killing. In this paper, we show that a lower bound on the Ricci curvature of the Riemannian manifold in the direction of geodesic vector field gives a sufficient condition for the geodesic vector field to be Killing. Also, we use a geodesic vector field on a 3-dimensional complete simply connected Riemannian manifold to find sufficient conditions to be isometric to a 3-sphere. We find a characterization of an Einstein manifold using a Killing vector field. Finally, it has been observed that a major source of geodesic vector fields is provided by solutions of Eikonal equations on a Riemannian manifold and we obtain a characterization of the Euclidean space using an Eikonal equation. 相似文献
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In this paper, we mainly investigate curvature properties and harmonicity of invariant vector fields on the four-dimensional Oscillator groups endowed with three left-invariant pseudo-Riemannian metrics of signature (2,2). We determine all harmonic vector fields, vector fields which define harmonic maps and the vector fields which are critical points for the energy functional restricted to vector fields of the same length. 相似文献
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Huang-jia Tian 《高校应用数学学报(英文版)》2014,29(2):217-229
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold. 相似文献
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Relying on the notion of set-valued Lie bracket introduced in an earlier paper, we extend some classical results valid for smooth vector fields to the case when the vector fields are just Lipschitz. In particular, we prove that the flows of two Lipschitz vector fields commute for small times if and only if their Lie bracket vanishes everywhere (i.e., equivalently, if their classical Lie bracket vanishes almost everywhere). We also extend the asymptotic formula that gives an estimate of the lack of commutativity of two vector fields in terms of their Lie bracket, and prove a simultaneous flow box theorem for commuting families of Lipschitz vector fields. 相似文献
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Some relations between the causal character of projective vector fields and curvature on a Lorentzian manifold M are studied. As a consequence, obstructions to the existence of such vector fields are found. Affine, homothetic and Killing vector fields are considered specifically. 相似文献
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C. M. Wood 《manuscripta mathematica》2000,101(1):71-88
The 3-dimensional Hopf vector field is shown to be a stable harmonic section of the unit tangent bundle. In contrast, higher
dimensional Hopf vector fields are unstable harmonic sections; indeed, there is a natural variation through smooth unit vector
fields which is locally energy-decreasing, and whose asymptotic limit is a singular vector field of finite energy. This energy
is explicitly calculated, and conjectured to be the infimum of the energy functional over all smooth unit vector fields.
Received: 17 March 1999 相似文献
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This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and linearization of vector fields near a hyperbolic singular point,in this paper,we deal with the case of hyperbolic vector fields on R3 by examining all possible resonant classes. 相似文献
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The purpose of this article is to characterize conformal vector fields with respect to the Sasaki metric tensor field on the
tangent bundle of a Riemannian manifold of dimension at least three. In particular, if the manifold in question is compact,
it is found that the only conformal vector fields are Killing vector fields. 相似文献
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Giovanni Calvaruso 《Central European Journal of Mathematics》2012,10(2):411-425
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of
the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields
are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified,
and the energy of these vector fields is explicitly calculated. 相似文献
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A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^*E of a vector bundle E over M([1]). In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E. 相似文献