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61.
The Geodesics of Metric Connections with Vectorial Torsion 总被引:1,自引:0,他引:1
The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields coincide with the Levi-Civita geodesics of a conformally equivalent metric. By pullback, this yields a systematic way of constructing invariants of motion for such connections from isometries of the conformally equivalent metric, and we explain in as much this result generalizes the Mercator projection which maps sphere loxodromes to straight lines in the plane. An example shows that Beltrami's theorem fails for this class of connections. We then study the system of differential equations describing geodesics in the plane for vector fields which are not gradients, and show among others that the Hopf–Rinow theorem does also not hold in general. 相似文献
62.
P. Witowicz 《Acta Mathematica Hungarica》2004,105(4):313-329
It is proved that non-degenerate surfaces in R
4 with planar geodesics are only the complex paraboloid and the product of two parabolas.
An erratum to this article is available at . 相似文献
63.
本文给出一类带由边界的调和映射的Liouville型定理,这种类型的定理在微分几何的一些问题中有十分重要的应用.我们通过对调和映射的能量选取特殊的变分族,得到任意从半空间的简单流形到一黎曼流形的带自由边界的调和映射在如果满足适当的条件(见定理)必为常值映射的结果. 相似文献
64.
Bing-ye WU Department of Mathematics Minjiang University Fuzhou China 《中国科学A辑(英文版)》2007,50(5):609-614
In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian. 相似文献
65.
A classical result in the theory of uniform spaces is that any topological space with a base of clopen sets admits a uniformity with a transitive base and the uniform topology of such a space has a base of clopen sets. This paper presents a pointfree generalization of this, both to uniform and quasi-uniform frames, together with various properties concerning total boundedness, compactifications and completions. 相似文献
66.
P. Danchev 《Lithuanian Mathematical Journal》2009,49(2):158-161
We prove that a special α-elongation of a totally projective group is an α-Σ-group if and only if it is a totally projective group. This parallels our recent result in [5]. 相似文献
67.
Let be a one-parameter family of positive integral operators on a locally compact space . For a possibly non-uniform partition of define a finite measure on the path space by using a) for the transition between any two consecutive partition times of distance and b) a suitable continuous interpolation scheme (e.g. Brownian bridges or geodesics). If necessary normalize the result
to get a probability measure. We prove a version of Chernoff's theorem of semigroup theory and tightness results which yield
convergence in law of such measures as the partition gets finer. In particular let be a closed smooth submanifold of a manifold . We prove convergence of Brownian motion on , conditioned to visit at all partition times, to a process on whose law has a density with respect to Brownian motion on which contains scalar, mean and sectional curvatures terms. Various approximation schemes for Brownian motion on are also given.
相似文献
68.
Hong Tam Judy 《应用数学和力学(英文版)》1995,16(6):533-537
This paper aims to determine the geodesic precession in Yu’s (Ω, Aab)-field theory[1], and to compare the result with that of the Schwarzschild orbit. 相似文献
69.
Martin Kohlmann 《Applicable analysis》2017,96(2):307-323
In the present paper, a two-component Camassa-Holm (2CH) system with vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims at presenting various details of the geometric formalism and a major result is the computation of the sectional curvature K of the underlying configuration manifold. As a further result, we show that there are directions for which K is strictly positive and bounded away from zero. 相似文献
70.
A. O. Asar 《代数通讯》2017,45(6):2690-2707
In this work the study of subgroups of totally imprimitive permutation groups is continued. Some sufficient conditions for the existence of minimal non-FC-subgroups are given. These results depend mainly on the properties of self-normalizing subgroups, which are closed in the topology of point-wise convergence. Finally, new properties of a totally imprimitive permutation p-group satisfying the cyclic-block property are given which might be a suitable example to look for minimal non-FC-subgroups. 相似文献