Dergiler / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 3

Some types of $f$-biharmonic and bi-$f$-harmonic curves

Sayfa
646–657
Yayın Tarihi
2022-06-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Besides, we obtain some nonexistence theorems.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal and $f$-biminimal in three-dimensional normal almost paracontact metric manifold.
📊
Temel Bulgular & Veri:In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal and $f$-biminimal in three-dimensional normal almost paracontact metric manifold.
💡
Sonuç & Katkı:Besides, we obtain some nonexistence theorems.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:non-Frenet Legendre curves · f-harmonic curves · f-biharmonic curves

Abstract

In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal and $f$-biminimal in three-dimensional normal almost paracontact metric manifold. Besides, we obtain some nonexistence theorems.

🔖

Bu Makaleye Atıf Yap

ERDOĞAN, F. E., BOZDAĞ, Ş. N. (2022). Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 3, 646–657. https://ajindex.com/articles/669190

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (22)

  1. M. Ara, Geometry of f-harmonic maps, Kodai Math. J. 22, 243–263, 1999
  2. C. Baikoussis and D.E. Blair, On Legendre curves in contact three-manifolds, Geom. Dedicata, 49 (2), 135–142, 1994
  3. P. Baird and J.C. Wood, Harmonic morphisms between Riemannian manifolds, Lond. Math. Soc. 29, Oxford Univ. Press, 2003
  4. M. Belkhelfa, I.E. Hirica, R. Rosca and L. Verstraelen,On Legendre curves in Riemannian and Lorentzian Sasaki Spaces, Soochow J. Math. 28 (1), 81–91, 2002
  5. D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics Vol. 203, Birkhauser, Boston, 2002
  6. C. Calin and M. Crasmareanu, Magnetic curves in three-dimensional quasi-para- Sasakian geometry, Mediterr. J. Math. 13, 2087–2097, 2016
  7. S.Y.A. Chang, L. Wang and P.C. Yang, A regularity theory of biharmonic maps, Comm. Pure Appl. Math. 52, 1113–1137, 1999
  8. N. Course, f-Harmonic maps, PhD Thesis, University of Warwick, 2004
  9. J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86, 109–160, 1964
  10. J. Eells and L. Lemaire, A report on harmonic maps, Bull. Lond. Math. Soc. 10, 1–68, 1978
  11. F. Gürler and C. Özgür, f-biminimal immersions, Turkish J. Math. 41, 564–575, 2017
  12. S. Izumiya and T. Nobuko, New special curves and developable surfaces, Turkish J. Math. 28 (2), 153–164, 2004
  13. G.Y. Jiang, 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 7, 389–402, 1986
  14. S. Kaneyuk and F.L. Willams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99, 173–187, 1985
  15. S. Keleş, S.Y. Perktaş and E. Kılıç, Biharmonic curves in Lorentzian Para-Sasakian Manifolds, Bull. Malays. Math. Sci. Soc. 33 (2), 325–344, 2010
  16. T. Lamm, Biharmonic map heat flow into manifolds of nonpositive curvature, Calc. Var. 22, 421–445, 2005
  17. E. Loubeau and S. Montaldo, Biminimal immersions, Proc. Edinb. Math. Soc. 51, 421-437, 2008
  18. W.J. Lu, On f-biharmonic maps and bi-f-harmonic maps between Riemannian manifolds, Sci. China Math. 58, 1483-1498, 2015
  19. W.J. Lu, On f-biharmonic maps between Riemannian manifolds, Sci. China Math. 58 (7) 1483–1498, 2015
  20. S. Montaldo and C. Oniciuc, A short survey on biharmonic maps between Riemannian manifolds, Rev. Un. Mat. Argentina, 47 (2), 1–22, 2006
  21. Y.L. Ou, On f -biharmonic maps and f -biharmonic submanifolds, Pacific J. Math. 271 (2), 461–477, 2014
  22. S. Ouakkas, R. Nasri and M. Djaa, On t