SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2023 / Cilt: 16 Sayı: 1

The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves

Mircea CRASMAREANU
Pages
225–231
Publication Date
2023-04-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A special attention is devoted to the examples, particularly to a horocycle provided by the null Lorentzian rotation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a new type of curvature function and associated evolute curve for a given curve in the hyperboloid model of plane hyperbolic geometry.
📊
Key Findings & Data:We introduce a new type of curvature function and associated evolute curve for a given curve in the hyperboloid model of plane hyperbolic geometry.
💡
Conclusion & Impact:A special attention is devoted to the examples, particularly to a horocycle provided by the null Lorentzian rotation.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:hyperbolic plane curve · flow-geodesic curvature · flow-evolute.

Abstract

We introduce a new type of curvature function and associated evolute curve for a given curve in the hyperboloid model of plane hyperbolic geometry. A special attention is devoted to the examples, particularly to a horocycle provided by the null Lorentzian rotation.

🔖

Cite This Article

CRASMAREANU, M. (2023). The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. International Electronic Journal of Geometry, Cilt: 16 Sayı: 1, 225–231. https://ajindex.com/articles/929614

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (2)

  1. Abdel-Aziz H. S.; Saad M. Khalifa; Abdel-Salam A. A., On involute-evolute curve couple in the hyperbolic and de Sitter spaces, J. Egypt. Math. Soc., 27(2019), paper po. 25, 18 p. Zbl 1430.53018 [2] Babaarslan Murat; Munteanu Marian Ioan, Time-like loxodromes on rotational surfaces in Minkowski 3-space, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si Mat., 61(2015), no. 2, 472-484. Zbl 1374.53034 [3] Crasmareanu Mircea, Magic conics, their integer points and complementary ellipses, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si Mat., 67(2021), no. 1, 129-148. Zbl 07621979 [4] Crasmareanu Mircea, The flow-curvature of spacelike parametrized curves in the Lorentz plane, Proceedings of the International Geometry Center, 15(2022), no. 2, 100-108. MR4503638 [5] Crasmareanu Mircea, The flow-curvature of plane parametrized curves, Commun. Fac. Sci. Univ. Ankara Ser. A1 Math. Stat., 72(2023), in press. [6] Crasmareanu Mircea, The flow-geodesic curvature and the flow-evolute of spherical curves, submitted. [7] Crasmareanu Mircea; Hre¸tcanu, Cristina-Elena, Golden differential geometry, Chaos Solitons Fractals, 38(2008), no. 5, 1229-1238. MR2456523 (2009k:53059) [8] Duggal Krishan L., Lorentzian geometry of globally framed manifolds, Acta Appl. Math., 19(1990), no. 2, 131-148. Zbl 0715.53045 [9] Duggal Krishan L., Harmonic maps, morphisms and globally null manifolds, Int. J. Pure Appl. Math., 6(2003), no. 4, 421-438. Zbl 1059.53050 [10] Duggal Krishan L., On scalar curvature in light-like geometry, J. Geom. Phys., 57(2007), no. 2, 473-481. Zbl 1107.53047 [11] Foreman Brendan, Vertex-type curves in constant angle surfaces of Hyp2 × R, in Suceav˘a, Bogdan D. (ed.) et al., Recent advances in the geometry of submanifolds: dedicated to the memory of Franki Dillen (1963–2013).
  2. Proceedings. Providence, RI: American Mathematical Society, Contemporary Mathematics 674, 49-57 (2016). Zbl 1360.53082 [12] Gábos Zoltán; Mester Agnes, Curves with constant geodesic curvature in the Bolyai-Lobachevskian plane, Stud. Univ. Babe¸s-Bolyai Math., 60(2015), no. 3, 463-470. Zbl 1374.53027