The Characterization of Affine Symplectic Curves in ℝ4

The Characterization of Affine Symplectic Curves in ℝ4

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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Bibliographic Details
Published in:Mathematics (Basel) Vol. 7; no. 1; p. 110
Main Authors: Çiçek Çetin, Esra, Bektaş, Mehmet
Format: Journal Article
Language:English
Published: Basel MDPI AG 01-01-2019
Subjects:
circular helices
Classical mechanics
Curves
Differential equations
Food science
Frenet frame
Geometrical optics
Geometry
Helices
Mathematical analysis
symplectic curvatures
symplectic curves
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7010110