黎曼流形上的测地线流和能量泛函

IF 0.2 Q4 MATHEMATICS

Italian Journal of Pure and Applied Mathematics Pub Date : 2021-10-12 DOI:10.11648/J.PAMJ.20211005.11

Yang Liu

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引用次数: 0

摘要

本文从对合的新角度研究了黎曼流形上的测地线流和能量泛函，证明了测地线具有极小能量，即能量泛函的极小值，并证明了测地线流是与黎曼流形切束上的正则辛结构有密切联系的哈密顿流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Geodesic Flow and Energy Functional on Riemannian Manifolds

In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold.

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来源期刊

Italian Journal of Pure and Applied Mathematics MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.