The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>

Symplectic geometry arises as the natural geometry of phase-space in the equations of classical mechanics. In this study, we obtain new characterizations of regular symplectic curves with respect to the Frenet frame in four-dimensional symplectic space. We also give the characterizations of the symp...

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Main Authors: Esra Çiçek Çetin, Mehmet Bektaş
Format: Article
Language:English
Published: MDPI AG 2019-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/7/1/110
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author Esra Çiçek Çetin
Mehmet Bektaş
author_facet Esra Çiçek Çetin
Mehmet Bektaş
author_sort Esra Çiçek Çetin
collection DOAJ
description Symplectic geometry arises as the natural geometry of phase-space in the equations of classical mechanics. In this study, we obtain new characterizations of regular symplectic curves with respect to the Frenet frame in four-dimensional symplectic space. We also give the characterizations of the symplectic circular helices as the third- and fourth-order differential equations involving the symplectic curvatures.
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spelling doaj.art-f12c2a61d64c4734b319984a3b833d0e2022-12-22T00:50:35ZengMDPI AGMathematics2227-73902019-01-017111010.3390/math7010110math7010110The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>Esra Çiçek Çetin0Mehmet Bektaş1Department of Mathematics, Faculty of Science, Firat University, 23119 Elazığ, TurkeyDepartment of Mathematics, Faculty of Science, Firat University, 23119 Elazığ, TurkeySymplectic geometry arises as the natural geometry of phase-space in the equations of classical mechanics. In this study, we obtain new characterizations of regular symplectic curves with respect to the Frenet frame in four-dimensional symplectic space. We also give the characterizations of the symplectic circular helices as the third- and fourth-order differential equations involving the symplectic curvatures.https://www.mdpi.com/2227-7390/7/1/110symplectic curvescircular helicessymplectic curvaturesFrenet frame
spellingShingle Esra Çiçek Çetin
Mehmet Bektaş
The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
Mathematics
symplectic curves
circular helices
symplectic curvatures
Frenet frame
title The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
title_full The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
title_fullStr The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
title_full_unstemmed The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
title_short The Characterization of Affine Symplectic Curves in ℝ<sup>4</sup>
title_sort characterization of affine symplectic curves in r sup 4 sup
topic symplectic curves
circular helices
symplectic curvatures
Frenet frame
url https://www.mdpi.com/2227-7390/7/1/110
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