Research Article
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Year 2023, , 225 - 231, 30.04.2023
https://doi.org/10.36890/iejg.1229215

Abstract

References

  • [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). 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

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

Year 2023, , 225 - 231, 30.04.2023
https://doi.org/10.36890/iejg.1229215

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.

References

  • [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). 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
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mircea Crasmareanu 0000-0002-5230-2751

Publication Date April 30, 2023
Acceptance Date February 20, 2023
Published in Issue Year 2023

Cite

APA Crasmareanu, M. (2023). The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. International Electronic Journal of Geometry, 16(1), 225-231. https://doi.org/10.36890/iejg.1229215
AMA Crasmareanu M. The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. Int. Electron. J. Geom. April 2023;16(1):225-231. doi:10.36890/iejg.1229215
Chicago Crasmareanu, Mircea. “The Flow-Geodesic Curvature and the Flow-Evolute of Hyperbolic Plane Curves”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 225-31. https://doi.org/10.36890/iejg.1229215.
EndNote Crasmareanu M (April 1, 2023) The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. International Electronic Journal of Geometry 16 1 225–231.
IEEE M. Crasmareanu, “The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 225–231, 2023, doi: 10.36890/iejg.1229215.
ISNAD Crasmareanu, Mircea. “The Flow-Geodesic Curvature and the Flow-Evolute of Hyperbolic Plane Curves”. International Electronic Journal of Geometry 16/1 (April 2023), 225-231. https://doi.org/10.36890/iejg.1229215.
JAMA Crasmareanu M. The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. Int. Electron. J. Geom. 2023;16:225–231.
MLA Crasmareanu, Mircea. “The Flow-Geodesic Curvature and the Flow-Evolute of Hyperbolic Plane Curves”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 225-31, doi:10.36890/iejg.1229215.
Vancouver Crasmareanu M. The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves. Int. Electron. J. Geom. 2023;16(1):225-31.

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