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Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane

Year 2024, Volume: 16 Issue: 1, 1 - 5, 30.06.2024
https://doi.org/10.47000/tjmcs.1403706

Abstract

We introduce four ordinary differential equations for a fixed natural parametrization of a spacelike curve $C$ in the Lorentz plane. The relationships between these differential equations is studied through the curvature of $C$.

References

  • Abe, N., Nakanishi, Y., Yamaguchi, S., Circles and spheres in pseudo-Riemannian geometry, Aequationes Math., 39(2-3)(1990), 134–145.
  • Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers, Open Math. 16(2018), 747–766.
  • Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane with curvature depending on their position, Open Math., 18(2020), 749–770.
  • Crasmareanu, M., The flow-curvature of spacelike parametrized curves in the Lorentz plane, Proc. Int. Geom. Cent., 15(2)(2022), 101–109.
  • Crasmareanu, M., The adjoint map of Euclidean plane curves and curvature problems, Tamkang J. Math., 55(2024), (in press).
  • Saloom, A., Tari, F., Curves in the Minkowski plane and their contact with pseudo-circles, Geom. Dedicata, 159(2012), 109–124.
  • Olver Peter J., Equivalence, Invariants, and Symmetry, Cambridge University Press, 1995.
  • Woolgar, E., Xie, R., Self-similar curve shortening flow in hyperbolic 2-space, Proc. Am. Math. Soc., 150(3)(2022), 1301–1319.
Year 2024, Volume: 16 Issue: 1, 1 - 5, 30.06.2024
https://doi.org/10.47000/tjmcs.1403706

Abstract

References

  • Abe, N., Nakanishi, Y., Yamaguchi, S., Circles and spheres in pseudo-Riemannian geometry, Aequationes Math., 39(2-3)(1990), 134–145.
  • Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers, Open Math. 16(2018), 747–766.
  • Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane with curvature depending on their position, Open Math., 18(2020), 749–770.
  • Crasmareanu, M., The flow-curvature of spacelike parametrized curves in the Lorentz plane, Proc. Int. Geom. Cent., 15(2)(2022), 101–109.
  • Crasmareanu, M., The adjoint map of Euclidean plane curves and curvature problems, Tamkang J. Math., 55(2024), (in press).
  • Saloom, A., Tari, F., Curves in the Minkowski plane and their contact with pseudo-circles, Geom. Dedicata, 159(2012), 109–124.
  • Olver Peter J., Equivalence, Invariants, and Symmetry, Cambridge University Press, 1995.
  • Woolgar, E., Xie, R., Self-similar curve shortening flow in hyperbolic 2-space, Proc. Am. Math. Soc., 150(3)(2022), 1301–1319.
There are 8 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Mircea Crasmareanu 0000-0002-5230-2751

Publication Date June 30, 2024
Submission Date December 12, 2023
Acceptance Date May 14, 2024
Published in Issue Year 2024 Volume: 16 Issue: 1

Cite

APA Crasmareanu, M. (2024). Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane. Turkish Journal of Mathematics and Computer Science, 16(1), 1-5. https://doi.org/10.47000/tjmcs.1403706
AMA Crasmareanu M. Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane. TJMCS. June 2024;16(1):1-5. doi:10.47000/tjmcs.1403706
Chicago Crasmareanu, Mircea. “Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 1-5. https://doi.org/10.47000/tjmcs.1403706.
EndNote Crasmareanu M (June 1, 2024) Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane. Turkish Journal of Mathematics and Computer Science 16 1 1–5.
IEEE M. Crasmareanu, “Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane”, TJMCS, vol. 16, no. 1, pp. 1–5, 2024, doi: 10.47000/tjmcs.1403706.
ISNAD Crasmareanu, Mircea. “Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 1-5. https://doi.org/10.47000/tjmcs.1403706.
JAMA Crasmareanu M. Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane. TJMCS. 2024;16:1–5.
MLA Crasmareanu, Mircea. “Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 1-5, doi:10.47000/tjmcs.1403706.
Vancouver Crasmareanu M. Differential Equations of Spacelike Parametrized Curves in the Lorentz Plane. TJMCS. 2024;16(1):1-5.