Integrable geodesic flow in 3D and webs of maximal rank

IF 1.4 3区 数学 Q1 MATHEMATICS
Sergey I. Agafonov
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引用次数: 0

Abstract

We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leaves are common zero directions of the integrals. We prove that, under some natural geometric hypothesis, the metric is of Stäckel type.

三维可积分大地流和最大秩网
我们用大地四维网来描述大地流的特征,即接纳两个具有共同主方向的相通二次积分,使得网叶的切线是积分的共同零方向。我们证明,在某些自然几何假设下,该公设属于 Stäckel 类型。
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来源期刊
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
期刊介绍: Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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