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f-Biminimal submanifolds of generalized space forms

Year 2019, Volume: 68 Issue: 2, 1301 - 1315, 01.08.2019
https://doi.org/10.31801/cfsuasmas.524498

Abstract

We study f-biminimal submanifolds in generalized complex space forms and generalized Sasakian space forms. Then, we analyze f-biminimal submanifolds in these spaces. Finally, we consider f-biminimal integral submanifolds in Sasakian space forms and give an example.

References

  • Alegre, P., Blair, D. E., Carriazo, A., Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157--183.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Boston. Birkhauser (2002).
  • Course N., f-harmonic maps, PhD, University of Warwick, Coventry, CV4 7AL, UK, (2004).
  • Eells, J. Jr., Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109--160.
  • Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C., Biharmonic submanifolds of CPⁿ, Math. Z., 266 (2010), 505 -- 531.
  • Fetcu, D., Oniciuc, C., Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific J. Math. 240 (2009), no. 1, 85--107.
  • Gürler F., Özgür C., f-Biminimal immersions, Turkish J. Math., 41 (2017), 564--575.
  • Jiang, G.Y., 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math., Ser. A 7(1986), 389--402.
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93--103.
  • Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie, 39 (1996), 183-198.
  • Loubeau, L., Montaldo S., Biminimal immersions, Proc. Edinb. Math. Soc., 51 (2008), 421-437.
  • Lu,W-J., On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds, Science China Math. 58 (2015), 1483-1498.
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geometry, 4 (1970) 237--244.
  • Olszak, Z., On the existence of generalized complex space forms, Israel J. Math., 65 (1989), no. 2, 214 -- 218.
  • Ouakkas S., Nasri R., Djaa M., On the f-harmonic and f-biharmonic maps. JP. J. Geom. Top. (1), 10 (2010), 11--27.
  • Ou Y-L., On f-biharmonic maps and f-biharmonic submanifolds, Pacific J. Math., 271 (2014), 461--477.
  • Roth, J., Upadhyay, A., Biharmonic submanifolds of generalized space forms, Diff. Geo. and Appl. 50 (2017), 88-104.
  • Roth, J., Upadhyay, A., f-Biharmonic and Bi-f-harmonic submanifolds of generalized space forms, arXiv:1609.08599 (2017).
  • Tricerri, F., Vanhecke, L., Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc., 267 (1981), no. 2, 365 -- 397.
  • Yano, K., Kon, M., Structures on manifolds, Series in Pure Mathematics. Singapore: World Scientific Publishing Co., (1984).
Year 2019, Volume: 68 Issue: 2, 1301 - 1315, 01.08.2019
https://doi.org/10.31801/cfsuasmas.524498

Abstract

References

  • Alegre, P., Blair, D. E., Carriazo, A., Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157--183.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Boston. Birkhauser (2002).
  • Course N., f-harmonic maps, PhD, University of Warwick, Coventry, CV4 7AL, UK, (2004).
  • Eells, J. Jr., Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109--160.
  • Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C., Biharmonic submanifolds of CPⁿ, Math. Z., 266 (2010), 505 -- 531.
  • Fetcu, D., Oniciuc, C., Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific J. Math. 240 (2009), no. 1, 85--107.
  • Gürler F., Özgür C., f-Biminimal immersions, Turkish J. Math., 41 (2017), 564--575.
  • Jiang, G.Y., 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math., Ser. A 7(1986), 389--402.
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93--103.
  • Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie, 39 (1996), 183-198.
  • Loubeau, L., Montaldo S., Biminimal immersions, Proc. Edinb. Math. Soc., 51 (2008), 421-437.
  • Lu,W-J., On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds, Science China Math. 58 (2015), 1483-1498.
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geometry, 4 (1970) 237--244.
  • Olszak, Z., On the existence of generalized complex space forms, Israel J. Math., 65 (1989), no. 2, 214 -- 218.
  • Ouakkas S., Nasri R., Djaa M., On the f-harmonic and f-biharmonic maps. JP. J. Geom. Top. (1), 10 (2010), 11--27.
  • Ou Y-L., On f-biharmonic maps and f-biharmonic submanifolds, Pacific J. Math., 271 (2014), 461--477.
  • Roth, J., Upadhyay, A., Biharmonic submanifolds of generalized space forms, Diff. Geo. and Appl. 50 (2017), 88-104.
  • Roth, J., Upadhyay, A., f-Biharmonic and Bi-f-harmonic submanifolds of generalized space forms, arXiv:1609.08599 (2017).
  • Tricerri, F., Vanhecke, L., Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc., 267 (1981), no. 2, 365 -- 397.
  • Yano, K., Kon, M., Structures on manifolds, Series in Pure Mathematics. Singapore: World Scientific Publishing Co., (1984).
There are 20 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Fatma Karaca This is me 0000-0002-0382-8028

Publication Date August 1, 2019
Submission Date January 10, 2018
Acceptance Date August 8, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Karaca, F. (2019). f-Biminimal submanifolds of generalized space forms. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1301-1315. https://doi.org/10.31801/cfsuasmas.524498
AMA Karaca F. f-Biminimal submanifolds of generalized space forms. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1301-1315. doi:10.31801/cfsuasmas.524498
Chicago Karaca, Fatma. “F-Biminimal Submanifolds of Generalized Space Forms”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1301-15. https://doi.org/10.31801/cfsuasmas.524498.
EndNote Karaca F (August 1, 2019) f-Biminimal submanifolds of generalized space forms. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1301–1315.
IEEE F. Karaca, “f-Biminimal submanifolds of generalized space forms”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1301–1315, 2019, doi: 10.31801/cfsuasmas.524498.
ISNAD Karaca, Fatma. “F-Biminimal Submanifolds of Generalized Space Forms”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1301-1315. https://doi.org/10.31801/cfsuasmas.524498.
JAMA Karaca F. f-Biminimal submanifolds of generalized space forms. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1301–1315.
MLA Karaca, Fatma. “F-Biminimal Submanifolds of Generalized Space Forms”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1301-15, doi:10.31801/cfsuasmas.524498.
Vancouver Karaca F. f-Biminimal submanifolds of generalized space forms. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1301-15.

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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