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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Then we give some results of solutions of these equations.
📌 3 Key Takeaways
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Objective & Hypothesis:The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve.
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Key Findings & Data:The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve.
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Conclusion & Impact:Then we give some results of solutions of these equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Elastic curve · Euler-Lagrange equation · pseudo spherical indicatrix
Abstract
The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski $3$-space. Then we give some results of solutions of these equations.
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Cite This Article
YÜCESAN, A., TÜKEL, G. Ö., TURHAN, T. (2018). Curves whose pseudo spherical indicatrices are elastic. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 6, 3123–3132. https://ajindex.com/articles/227824