Framed curves in three-dimensional Lie groups and a Berry phase model

被引：7

作者：

Yazici, Bahar Dogan ^{[1
]}

Okuyucu, Osman Zeki ^{[1
]}

Tosun, Murat ^{[2
]}

机构：

[1] Bilecik Seyh Edebali Univ, Dept Math, TR-11200 Bilecik, Turkey

[2] Sakarya Univ, Dept Math, TR-54000 Sakarya, Turkey

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2022年 / 182卷

关键词：

Lie groups; Framed curves; Adapted frames; Optical fiber; Berry; -phase; Polarization vector;

D O I：

10.1016/j.geomphys.2022.104682

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, we introduce framed curves which can have singular points in three-dimensional Lie groups. We give Frenet-Serret type formulas of framed curves with the help of a Lie curvature in three-dimensional Lie groups. Then, we define adapted frames of framed curves in three-dimensional Lie groups such that Frenet-Serret type frame and Bishop frame. Finally, as a physical application, we give Berry phase model of polarized light wave along an optical fiber in Lie groups. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：12

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