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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MDPI AG
2019-01-01
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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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format | Article |
id | doaj.art-f12c2a61d64c4734b319984a3b833d0e |
institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-12-11T21:16:14Z |
publishDate | 2019-01-01 |
publisher | MDPI AG |
record_format | Article |
series | Mathematics |
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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