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Year 2023, Volume: 11 Issue: 1, 70 - 76, 30.04.2023

Şerife Nur Bozdağ Selcen Yüksel Perktaş Feyza Esra Erdoğan

Abstract

Keywords

$f$-biminimal curves generalized Sasakian space forms Legendre curves

References

  • [1] P. Alegre, D. E. Blair, A. Carriazo, Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157–183.
  • [2] M. Ara, Geometry of f-harmonic maps, Kodai Mathematical Journal, 22(2) (1999), 243–263.
  • [3] S¸ . N. Bozda˘g, F. E. Erdo˘gan, f -Biharmonic and bi-f-harmonic magnetic curves in three-dimensional normal almost paracontact metric manifolds, Int. Electronic Journal of Geometry, 14(2) (2021), 331-347.
  • [4] S¸ . N. Bozda˘g, F. E. Erdo˘gan, On f -Biharmonic and bi- f -Harmonic Frenet Legendre Curves, Int. J. Maps Math. 5(2) (2022), 112-138.
  • [5] N. Course, f -harmonic maps, Ph.D. Thesis, University of Warwick, (2004).
  • [6] Y. J. Chiang, f -biharmonic maps between Riemannian manifolds, In Proc. of the Fourteenth Int. Conference on Geometry, Integrability and Quantization, (2013), 74-86.
  • [7] J. Eells, J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160.
  • [8] F. E. Erdo˘gan, S¸ . N. Bozda˘g, Some types of f -biharmonic and bi- f -harmonic curves, Hacettepe Journal of Mathematics and Statistics, 51(3) (2022), 646 - 657.
  • [9] D. Fetcu, Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc., 45 (2008), 393–404. [10] D. Fetcu, C. Oniciuc, Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pac. J. Math., 240 (2009), 85–107.
  • [11] F. Gu¨rler, C. O¨ zgu¨r, f -Biminimal immersions, Turkish Journal of Mathematics, 41(3) (2017), 564–575.
  • [12] S¸ . Gu¨venc¸, C. O¨ zgu¨r, On the characterizations of f-biharmonic Legendre curves in Sasakian space forms, Filomat, 31(3) (2017), 639–648.
  • [13] F. Karaca, f -Biminimal submanifolds of generalized space forms, Com. Faculty of Sci. Uni. of Ankara Series A1 Math. and Sta., 68(2) (2019), 1301–1315.
  • [14] L. Loubeau, S. Montaldo, Biminimal immersions, Proc. Edinb. Math. Soc., 51 (2008) 421–437.
  • [15] C. O¨ zgu¨r, S¸ . Gu¨venc¸, On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collect. Math., 65 (2014), 203–218.
  • [16] J. Roth, A. Upadhyay, f-biharmonic and bi-f-harmonic submanifolds of generalized space forms, arXiv:1609.08599v1, (2016).
  • [17] J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193.
  • [18] J. Roth, U. Abhitosh, f -biharmonic submanifolds of generalized space forms, Results in Mathematics, 75(1) (2020), 1–25.

On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms

Year 2023, Volume: 11 Issue: 1, 70 - 76, 30.04.2023

Şerife Nur Bozdağ Selcen Yüksel Perktaş Feyza Esra Erdoğan

Abstract

In this paper, $f$-biminimal Legendre curves are studied in $(\protect\alpha ,\protect\beta )$-trans Sasakian generalized Sasakian space forms. Necessary and sufficient conditions are obtained for a Legendre curve to be $f$-biminimal in such space forms . Besides, some special cases are studied and some nonexistence theorems are obtained.

Keywords

$f$-biminimal curves generalized Sasakian space forms Legendre curves

References

  • [1] P. Alegre, D. E. Blair, A. Carriazo, Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157–183.
  • [2] M. Ara, Geometry of f-harmonic maps, Kodai Mathematical Journal, 22(2) (1999), 243–263.
  • [3] S¸ . N. Bozda˘g, F. E. Erdo˘gan, f -Biharmonic and bi-f-harmonic magnetic curves in three-dimensional normal almost paracontact metric manifolds, Int. Electronic Journal of Geometry, 14(2) (2021), 331-347.
  • [4] S¸ . N. Bozda˘g, F. E. Erdo˘gan, On f -Biharmonic and bi- f -Harmonic Frenet Legendre Curves, Int. J. Maps Math. 5(2) (2022), 112-138.
  • [5] N. Course, f -harmonic maps, Ph.D. Thesis, University of Warwick, (2004).
  • [6] Y. J. Chiang, f -biharmonic maps between Riemannian manifolds, In Proc. of the Fourteenth Int. Conference on Geometry, Integrability and Quantization, (2013), 74-86.
  • [7] J. Eells, J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160.
  • [8] F. E. Erdo˘gan, S¸ . N. Bozda˘g, Some types of f -biharmonic and bi- f -harmonic curves, Hacettepe Journal of Mathematics and Statistics, 51(3) (2022), 646 - 657.
  • [9] D. Fetcu, Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc., 45 (2008), 393–404. [10] D. Fetcu, C. Oniciuc, Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pac. J. Math., 240 (2009), 85–107.
  • [11] F. Gu¨rler, C. O¨ zgu¨r, f -Biminimal immersions, Turkish Journal of Mathematics, 41(3) (2017), 564–575.
  • [12] S¸ . Gu¨venc¸, C. O¨ zgu¨r, On the characterizations of f-biharmonic Legendre curves in Sasakian space forms, Filomat, 31(3) (2017), 639–648.
  • [13] F. Karaca, f -Biminimal submanifolds of generalized space forms, Com. Faculty of Sci. Uni. of Ankara Series A1 Math. and Sta., 68(2) (2019), 1301–1315.
  • [14] L. Loubeau, S. Montaldo, Biminimal immersions, Proc. Edinb. Math. Soc., 51 (2008) 421–437.
  • [15] C. O¨ zgu¨r, S¸ . Gu¨venc¸, On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collect. Math., 65 (2014), 203–218.
  • [16] J. Roth, A. Upadhyay, f-biharmonic and bi-f-harmonic submanifolds of generalized space forms, arXiv:1609.08599v1, (2016).
  • [17] J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193.
  • [18] J. Roth, U. Abhitosh, f -biharmonic submanifolds of generalized space forms, Results in Mathematics, 75(1) (2020), 1–25.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Şerife Nur Bozdağ

Selcen Yüksel Perktaş

Feyza Esra Erdoğan

Publication Date April 30, 2023
Submission Date February 22, 2023
Acceptance Date April 6, 2023
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Bozdağ, Ş. N., Yüksel Perktaş, S., & Erdoğan, F. E. (2023). On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms. Konuralp Journal of Mathematics, 11(1), 70-76.
AMA Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE. On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms. Konuralp J. Math. April 2023;11(1):70-76.
Chicago Bozdağ, Şerife Nur, Selcen Yüksel Perktaş, and Feyza Esra Erdoğan. “On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 70-76.
EndNote Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE (April 1, 2023) On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms. Konuralp Journal of Mathematics 11 1 70–76.
IEEE Ş. N. Bozdağ, S. Yüksel Perktaş, and F. E. Erdoğan, “On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms”, Konuralp J. Math., vol. 11, no. 1, pp. 70–76, 2023.
ISNAD Bozdağ, Şerife Nur et al. “On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms”. Konuralp Journal of Mathematics 11/1 (April 2023), 70-76.
JAMA Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE. On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms. Konuralp J. Math. 2023;11:70–76.
MLA Bozdağ, Şerife Nur et al. “On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 70-76.
Vancouver Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE. On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms. Konuralp J. Math. 2023;11(1):70-6.
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