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

DOĞAN YAZICI, BAHAR; OKUYUCU, OSMAN; Tosun, Murat

doi:10.1016/j.geomphys.2022.104682

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

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DOĞAN YAZICI B., OKUYUCU O. Z., Tosun M.

Journal of Geometry and Physics, vol.182, 2022 (SCI-Expanded)

Publication Type: Article / Article
Volume: 182
Publication Date: 2022
Doi Number: 10.1016/j.geomphys.2022.104682
Journal Name: Journal of Geometry and Physics
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
Keywords: Adapted frames, Berry-phase, Framed curves, Lie groups, Optical fiber, Polarization vector
Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2022 Elsevier B.V.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.