双拉格朗日结构和射线空间

IF 2 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-07-31 DOI:10.1088/1751-8121/ad65a4

Wojciech Domitrz, Marcin Zubilewicz

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引用次数: 0

摘要

本文重点研究与双拉格朗日结构相关的局部曲率不变式。我们在之前关于无发散网的发现（Domitrz and Zubilewicz 2023 Anal.）针对塔巴奇尼科夫（1993 Differ. Geom. Appl.3，265-84）提出的问题，我们提供了两个问题的完整解决方案：一对超曲面诱导的射线空间内平面双拉格朗日结构的存在性，以及交错平面内拉格朗日曲线切线诱导的平面双拉格朗日结构的存在性。

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Bi-Lagrangian structures and the space of rays

This paper focuses on local curvature invariants associated with bi-Lagrangian structures. We establish several geometric conditions that determine when the canonical connection is flat, building on our previous findings regarding divergence-free webs (Domitrz and Zubilewicz 2023 Anal. Math. Phys. 13 4). Addressing questions raised by Tabachnikov (1993 Differ. Geom. Appl. 3 265–84), we provide complete solutions to two problems: the existence of flat bi-Lagrangian structures within the space of rays induced by a pair of hypersurfaces, and the existence of flat bi-Lagrangian structures induced by tangents to Lagrangian curves in the symplectic plane.

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来源期刊

Journal of Physics A: Mathematical and Theoretical 物理-物理：数学物理

CiteScore

4.10

自引率

14.30%

发文量

542

审稿时长

1.9 months

期刊介绍： Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.