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III-harmonic Curves in 


SL2ℝ˜
\widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}}

 Space Cover

III-harmonic Curves in  SL2ℝ˜ \widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} Space

Open Access
|Dec 2024

References

  1. A. T. Ali, Position vectors of general helices in Euclidean 3-space, Bull. Math. Anal. Appl. 3 (2011), 1-8.
  2. M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997), 1503-1509.
  3. M. Barros, A. Ferrández, P. Lucas, M. A. Meroño, General helices in the 3-dimensional Lorentzian space forms, Rocky Mountain J. Math. 31 (2001), 373-388.
  4. V. Branding, A structure theorem for polyharmonic maps between Riemannian manifolds, arXiv preprint arXiv:1901.08445, 2019.
  5. R. Caddeo, C. Oniciuc, P. Piu, Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group, Rend. Sem. Mat. Univ. Pol. Torino 62 (3) (2004), 265-278.
  6. R. Caddeo, S. Montaldo, C. Oniciuc, P. Piu, The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces, Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca (2006), 121-131.
  7. [7] B. Divjak, Z. Erjavec, B. Szabolcs, B. Szilágyi, Geodesics and geodesic spheres in SL(2,)˜ \widetilde {SL\left( {2,\mathbb{R}} \right)} geometry, Math. Commun. 14 (2009), 413-424.
  8. J. Eells, L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics 50, 1983.
  9. [9] Z. Erjavec, D. Horvat, Biharmonic curves in SL(2,)˜ \widetilde {SL\left( {2,\mathbb{R}} \right)} space, Math. Commun. 19 (2014), 291-299.
  10. [10] Z. Erjavec, Minimal surfaces in SL(2,)˜ \widetilde {SL\left( {2,\mathbb{R}} \right)} geometry, Glas. Mat. 50 (2015), 207-221.
  11. D. Fetcu, Biharmonic curves in Cartan-Vranceanu (2n+1)-dimensional spaces, Beitr. Algebra Geom. 46 (2) (2007), 513-521.
  12. S. Maeta, k-Harmonic maps into a Riemannian manifold with constant sectional curvature, Proc. Amer. Math. Soc. 140 (2012), 1835-1847.
  13. S. Maeta, The second variational formula of the k-energy and k-harmonic curves, Osaka J. Math. 49 (2012), 1035-1063.
  14. E. Molnár, The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom. 38 (1997), 261-288.
  15. E. Molnár, J. Szirmai, Symmetries in the 8 homogeneous 3− geometries, Symmetry Cult. Sci. 21 (2010), 87-117.
  16. E. Molnár, J. Szirmai, A. Vesnin, The optimal packings by translation balls in SL(2, ℝ), J. Geom. 105 (2014), 287-306.
  17. S. Montaldo, A. Pampano, Triharmonic curves in 3-dimensional homogeneous spaces, Mediterr. J. Math. 18 (2021), Article number 198.
  18. S. Montaldo, C. Oniciuc, A. Ratto, Polyharmonic surfaces in 3-dimensional homogeneous spaces, Manuscripta Math. 174 (2024), 31-58.
  19. S. Montaldo A. Ratto, New examples of r- harmonic immersions into the sphere, J. Math. Anal. Appl. 458 (1) (2018), 849-859.
  20. J. Monterde, Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana 13 (2007), 177-186.
  21. B. Senoussi, Triharmonic curves in Heisenberg group H3, J. Dyn. Syst. Geom. Theor. 20 (2022), 55-65.
  22. B. Senoussi, Triharmonic curves in SOL3 space, Palestine J. Math. 11, (2022), 264-273.
  23. B. Senoussi, Triharmonic curves in Bianchi-Cartan-Vranceanu spaces, Rendiconti Sem. Mat. Univ. Pol. Torino 80 (2) (2022), 5-13.
  24. B. Senoussi, M. Bekkar, Characterization of general helix in the 3- dimensional Lorentz-Heisenberg space, Int. Electron. J. Geom. 6 (1) (2013), 46-55.
  25. [25] B. Senoussi, M. Bekkar, Some characterization of curves in SL2˜ \widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} space, Sib. Elektron. Mat. Izv. 16 (2019), 902-915.
  26. D. J. Struik, Lectures on classical di erential geometry, New York Dover Publications. Inc., 1988.
  27. S. B. Wang, The first variation formula for k-harmonic mapping, J. Nanchang Univ. 13 (1989).
DOI: https://doi.org/10.2478/awutm-2024-0010 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Submitted on: Jan 4, 2024
Accepted on: Dec 9, 2024
Published on: Dec 24, 2024
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2024 Bendehiba Senoussi, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.