边界处接近测地线的黎曼立方

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI:10.3934/jgm.2022003

M. Camarinha, F. Silva Leite, P. Crouch

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引用次数: 4

摘要

本文研究了在位置和速度边界条件下黎曼三次方程组的存在唯一性。我们将研究限制在边界处接近测地线的立方体。换句话说，我们在测地线边界数据的邻域中考虑边界数据。我们定义一个映射来推广黎曼指数，双指数。该图用于建立初始数据和边界数据之间的对应关系。我们还利用双指数映射强调了双共轭点与沿立方的双雅可比场之间的关系。

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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Riemannian cubics close to geodesics at the boundaries

In this paper we investigate the existence and uniqueness of Riemannian cubics under boundary conditions on position and velocity. We restrict the study to cubics close to geodesics at the boundaries. In other words, we consider the boundary data in a neighborhood of geodesic boundary data. We define a map that generalizes the Riemannian exponential, the biexponential. This map is used to establish the correspondence between initial and boundary data. We also emphasize the relation between biconjugate points and bi-Jacobi fields along cubics by means of the biexponential map.

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.