We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.
📌 3 Key Takeaways
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Objective & Hypothesis:We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.
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Key Findings & Data:We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.
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Conclusion & Impact:We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.
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Cite This Article
GÖRGÜLÜ, A., GÜRBÜZ, N. (2022). Intrinsic equations for a relaxed elastic line on an oriented hypersurface in the Minkowski space $Bbb{R}^n_1$. Turkish Journal of Mathematics, Cilt: 24 - Sayı: 3, 283–294. https://ajindex.com/articles/608949
Gürbüz N., Görgülü A., "Intrinsic equations for a relaxed elastic line on an oriented surface in the Minkowski space $Bbb{R}^3_1$," Hadronic Journal 23, 143-163 (2000)
H.K. Nickerson, Manning Gerald., "Intrinsic equations for a relaxed elastic line on an oriented surface", Geometriae Dedicate 27(1988), 127-136
O'Neill, B., 1983, Semi-Riemannian Geometry, Acedemic Press. New York,London.