Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 51 Sayı: 3, 646 - 657, 01.06.2022
https://doi.org/10.15672/hujms.804821

Öz

Kaynakça

  • [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 the f-harmonic and f-biharmonic maps, JP J. Geom. Topol. 10, 11–27, 2010.
  • [23] S.Y. Perktaş and B.E. Acet, Biharmonic Frenet and non-Frenet Legendre curves in three-dimensional normal almost paracontact metric manifolds, AIP Conference Proceedings, 1833 (1), p. 020025, 2017.
  • [24] S.Y. Perktaş, A.M. Blaga, B.E. Acet and F.E. Erdoğan, Magnetic biharmonic curves on three-dimensional normal almost paracontact metric manifolds, AIP Conference
  • Proceedings, 1991, p. 020004, 2018. [25] S.Y. Perktaş, A.M. Blaga, F.E. Erdoğan and B.E. Acet, Bi-f-Harmonic curves and hypersurfaces, Filomat, 33 (16), 5167–5180, 2019.
  • [26] J. Roth and A. Upadhyay, f-biharmonic and bi-f-harmonic submanifolds of generalized space forms, arXiv. 1609.08599, 2016.
  • [27] P. Strzelecki, On biharmonic maps and their generalizations, Calc. Var. 18, 401–432, 2003.
  • [28] C. Wang, Biharmonic maps from R4 into a Riemannian manifold, Math. Z. 247, 65–87, 2004.
  • [29] C. Wang, Remarks on biharmonic maps into spheres, Calc. Var. 21, 221–242, 2004.
  • [30] J. Welyczko, On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math. 33 (4), 929–937, 2007.
  • [31] J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results Math. 54, 377–387, 2009.
  • [32] S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo. 36, 37–60, 2009.
  • [33] C.L. Zhao and W.L. Lu, Bi-f-harmonic map equations on singly warped product manifolds, Appl. Math. J. Chinese Univ. 30 (1), 111–126, 2015.

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

Yıl 2022, Cilt: 51 Sayı: 3, 646 - 657, 01.06.2022
https://doi.org/10.15672/hujms.804821

Öz

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.

Kaynakça

  • [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 the f-harmonic and f-biharmonic maps, JP J. Geom. Topol. 10, 11–27, 2010.
  • [23] S.Y. Perktaş and B.E. Acet, Biharmonic Frenet and non-Frenet Legendre curves in three-dimensional normal almost paracontact metric manifolds, AIP Conference Proceedings, 1833 (1), p. 020025, 2017.
  • [24] S.Y. Perktaş, A.M. Blaga, B.E. Acet and F.E. Erdoğan, Magnetic biharmonic curves on three-dimensional normal almost paracontact metric manifolds, AIP Conference
  • Proceedings, 1991, p. 020004, 2018. [25] S.Y. Perktaş, A.M. Blaga, F.E. Erdoğan and B.E. Acet, Bi-f-Harmonic curves and hypersurfaces, Filomat, 33 (16), 5167–5180, 2019.
  • [26] J. Roth and A. Upadhyay, f-biharmonic and bi-f-harmonic submanifolds of generalized space forms, arXiv. 1609.08599, 2016.
  • [27] P. Strzelecki, On biharmonic maps and their generalizations, Calc. Var. 18, 401–432, 2003.
  • [28] C. Wang, Biharmonic maps from R4 into a Riemannian manifold, Math. Z. 247, 65–87, 2004.
  • [29] C. Wang, Remarks on biharmonic maps into spheres, Calc. Var. 21, 221–242, 2004.
  • [30] J. Welyczko, On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math. 33 (4), 929–937, 2007.
  • [31] J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results Math. 54, 377–387, 2009.
  • [32] S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo. 36, 37–60, 2009.
  • [33] C.L. Zhao and W.L. Lu, Bi-f-harmonic map equations on singly warped product manifolds, Appl. Math. J. Chinese Univ. 30 (1), 111–126, 2015.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Feyza Esra Erdoğan 0000-0003-0568-7510

Şerife Nur Bozdağ 0000-0002-9651-7834

Yayımlanma Tarihi 1 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 3

Kaynak Göster

APA Erdoğan, F. E., & Bozdağ, Ş. N. (2022). Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics, 51(3), 646-657. https://doi.org/10.15672/hujms.804821
AMA Erdoğan FE, Bozdağ ŞN. Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics. Haziran 2022;51(3):646-657. doi:10.15672/hujms.804821
Chicago Erdoğan, Feyza Esra, ve Şerife Nur Bozdağ. “Some Types of $f$-Biharmonic and Bi-$f$-Harmonic Curves”. Hacettepe Journal of Mathematics and Statistics 51, sy. 3 (Haziran 2022): 646-57. https://doi.org/10.15672/hujms.804821.
EndNote Erdoğan FE, Bozdağ ŞN (01 Haziran 2022) Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics 51 3 646–657.
IEEE F. E. Erdoğan ve Ş. N. Bozdağ, “Some types of $f$-biharmonic and bi-$f$-harmonic curves”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 3, ss. 646–657, 2022, doi: 10.15672/hujms.804821.
ISNAD Erdoğan, Feyza Esra - Bozdağ, Şerife Nur. “Some Types of $f$-Biharmonic and Bi-$f$-Harmonic Curves”. Hacettepe Journal of Mathematics and Statistics 51/3 (Haziran 2022), 646-657. https://doi.org/10.15672/hujms.804821.
JAMA Erdoğan FE, Bozdağ ŞN. Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics. 2022;51:646–657.
MLA Erdoğan, Feyza Esra ve Şerife Nur Bozdağ. “Some Types of $f$-Biharmonic and Bi-$f$-Harmonic Curves”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 3, 2022, ss. 646-57, doi:10.15672/hujms.804821.
Vancouver Erdoğan FE, Bozdağ ŞN. Some types of $f$-biharmonic and bi-$f$-harmonic curves. Hacettepe Journal of Mathematics and Statistics. 2022;51(3):646-57.