Some New Characterizations of Symplectic Curve in 4-Dimensional Symplectic Space

Year 2019, Volume: 2 Issue: 4, 331 - 334, 29.12.2019

Esra Çiçek Çetin Mehmet Bektaş

https://doi.org/10.33434/cams.643076

Cited By: 2

Abstract

It is well known that there exist characterizations for curve in Euclidean space.$\ $Also, a lot of authors extended this characterizations for Minkowski space and obtained very different results. In this paper, we introduce the geometric properties of Symplectic Curve in $% 4$-Dimensional Symplectic Space which given by \cite{7,10}. Later we obtained the conditions for Symplectic Curve to lie on some subspaces of $% 4$-Dimensional Symplectic Space and we give some characterizations and theorems for these curves.

Keywords

Symplectic curve, Symplectic space

References

• [1] N. Kamran, P. Olver, K. Tenenblat, Local symplectic invariants for curves, Commun. Contemp. Math., 11(2) (2009), 165-183.
• [2] F. Valiquette, Geometric affine symplectic curve flows in R4, Differ. Geom. Appl., 30(6) (2012), 631-641.
• [3] S.S. Chern, H. C. Wang, Differential geometry in symplectic space. I, Sci. Rep. Nat. Tsing Hua Univ., 4 (1947), 453-477.
• [4] J.C. Alvarez Paiva, C. E. Duran, Geometric invariants of fanning curves, Adv. Appl. Math., 42(3) (2009), 290-312.
• [5] V. Deconchy, Hypersurfaces in symplectic affine geometry, Differ. Geom. Appl., 17(1) (2002), 1-13.
• [6] E. Musso, L. Nicolodi, Symplectic applicability of Lagrangian surfaces, Sigma, 5 (2009), 067, 18 pages.
• [7] E. Musso, E.G. Hubert, Lagrangian Curves in a 4-Dimensional Affine Symplectic Space, Acta Appl. Math., 134(1) (2014) 133-160.
• [8] M. Fels, P. J. Olver, Moving coframes, I. A practic algorithm, Acta Appl. Math., 51 (1998), 161-213.
• [9] M. Fels, P. J. Olver, Moving coframes, II. regularization and theoretical foundation, Acta Appl. Math., 55 (1999), 127-208. [10] M.A. Akgün, A. İ. Sivridağ, E. Kılıç, The characterizations of a Spacelike Curve in R^41_ , Konuralp J. Math., 4(2) (2016), 299-307.