Research Article
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Year 2021, Volume: 70 Issue: 1, 52 - 63, 30.06.2021
https://doi.org/10.31801/cfsuasmas.699780

Abstract

Project Number

09/028(1010)/2017-EMR-1

References

  • Arslan, K., Murathan, C., Özgür, C., Yildiz, A., Pseudosymmetric contact metric manifolds in the sense of M. C. Chaki, Proc. Estonian Acad. Sci. Phys. Math., 50 (2001), 124-132.
  • Blair, D. E., Contact Manifold in Riemannian Geometry, Lecture Notes on Mathematics, Springer, Berlin, 509, 1976.
  • Blair, D. E., Riemannian Geometry on contact and symplectic manifolds, Progr. Math., Birkhäuser, Boston, 203, 2010.
  • De, U. C., Mandal, K., On a type of almost Kenmotsu manifolds with nullity distributions, Arab J. Math. Sci., 23 (2017), 109-123.
  • Dey, D. Majhi, P., On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions, Facta Univ. Ser. Math. Inform., 33 (2018), 255-268.
  • Dileo, G., Pastore, A.M., Almost Kenmotsu manifolds and nullity distributions, J. Geom., 93 (2009), 46-61.
  • Dileo, G., Pastore, A.M., , Almost Kenmotsu manifolds with a condition of η-parallelsim, Differential Geom. Appl., 27 (2009), 671-679.
  • Dileo, G., Pastore, A.M., , Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343-354.
  • Ghosh, A., Sharma, R., Sasakian manifolds with purely transversal Bach tensor, J. Math. Phys., 58, (2017), 103502.
  • Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicta, 7 (1978), 259-280.
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
  • Özgür, C., On weakly symmetric Kenmotsu manifolds, Diff. Geom. Dyn. Syst., 8 (2016), 204-209.
  • Özen, F., Altay, S., On weakly and pseudo-symmetric Riemannian spaces, Indian J. Pure Appl. Math., 33 (2002), 1477-1488.
  • Pastore, A.M., Saltarelli, V., Generalized nullity distribution on almost Kenmotsu manifolds, Int. Elec. J. Geom. 4 (2011), 168-183.
  • Pérez, J.D., Lee, H., Suh, Y.J., Woo, C., Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor in the GTW connection, Canad. Math. Bull., (2016), 721-733.
  • Sahin, B., Yildiz, A., Chaki type pseudo-symmetric lightlike hypersurfaces, Int. J. Geom. Methods Mod. Phys., 12 (2015), 1550051, 19 pp.
  • Verstraelen, L., Comments on pseudosymmetry in the sense of Ryszard Deszcz, Geometry and topology of submanifolds, VI. River Edge, NJ: World Sci. Publishing, (1994), 199-209.
  • Wang, Y., Liu, X., On φ-recurrent almost Kenmotsu manifolds, Kuwait J. Sci., 42 (2015), 65-77.
  • Wang, Y., Liu, X., On a type of almost Kenmotsu manifolds with harmonic curvature tensors, Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), 15-24.
  • Wang, Y., Cotton tensor on almost cokähler 3-manifolds, Ann. Polon. Math., 120(2) (2017).
  • Zhen, G., Cabrerizo, J. L., Fernández, L.M., Fernández, M., On ξ-conformally flat contact metric manifolds, Indian J. Pure Appl. Math., 28 (1997), 725-734.

A classification of $(k,\mu)'$-almost Kenmotsu manifolds admitting Cotton tensor

Year 2021, Volume: 70 Issue: 1, 52 - 63, 30.06.2021
https://doi.org/10.31801/cfsuasmas.699780

Abstract

The object of the present paper is to classify $(k,\mu)'$-almost Kenmotsu manifolds admitting Cotton tensors. We characterize $(k,\mu)'$-almost Kenmotsu manifolds with vanishing and parallel Cotton tensors. Beside this, $(k,\mu)'$-almost Kenmotsu manifolds satisfying Cotton semisymmetry and $Q(g,C) = 0$ are studied. Further, Cotton pseudo-symmetric $(k,\mu)'$-almost Kenmotsu manifolds are classified.

Supporting Institution

Council of Scientific and Industrial Research, India

Project Number

09/028(1010)/2017-EMR-1

Thanks

The author Dibakar Dey is thankful to CSIR, India for their assistance.

References

  • Arslan, K., Murathan, C., Özgür, C., Yildiz, A., Pseudosymmetric contact metric manifolds in the sense of M. C. Chaki, Proc. Estonian Acad. Sci. Phys. Math., 50 (2001), 124-132.
  • Blair, D. E., Contact Manifold in Riemannian Geometry, Lecture Notes on Mathematics, Springer, Berlin, 509, 1976.
  • Blair, D. E., Riemannian Geometry on contact and symplectic manifolds, Progr. Math., Birkhäuser, Boston, 203, 2010.
  • De, U. C., Mandal, K., On a type of almost Kenmotsu manifolds with nullity distributions, Arab J. Math. Sci., 23 (2017), 109-123.
  • Dey, D. Majhi, P., On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions, Facta Univ. Ser. Math. Inform., 33 (2018), 255-268.
  • Dileo, G., Pastore, A.M., Almost Kenmotsu manifolds and nullity distributions, J. Geom., 93 (2009), 46-61.
  • Dileo, G., Pastore, A.M., , Almost Kenmotsu manifolds with a condition of η-parallelsim, Differential Geom. Appl., 27 (2009), 671-679.
  • Dileo, G., Pastore, A.M., , Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343-354.
  • Ghosh, A., Sharma, R., Sasakian manifolds with purely transversal Bach tensor, J. Math. Phys., 58, (2017), 103502.
  • Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicta, 7 (1978), 259-280.
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
  • Özgür, C., On weakly symmetric Kenmotsu manifolds, Diff. Geom. Dyn. Syst., 8 (2016), 204-209.
  • Özen, F., Altay, S., On weakly and pseudo-symmetric Riemannian spaces, Indian J. Pure Appl. Math., 33 (2002), 1477-1488.
  • Pastore, A.M., Saltarelli, V., Generalized nullity distribution on almost Kenmotsu manifolds, Int. Elec. J. Geom. 4 (2011), 168-183.
  • Pérez, J.D., Lee, H., Suh, Y.J., Woo, C., Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor in the GTW connection, Canad. Math. Bull., (2016), 721-733.
  • Sahin, B., Yildiz, A., Chaki type pseudo-symmetric lightlike hypersurfaces, Int. J. Geom. Methods Mod. Phys., 12 (2015), 1550051, 19 pp.
  • Verstraelen, L., Comments on pseudosymmetry in the sense of Ryszard Deszcz, Geometry and topology of submanifolds, VI. River Edge, NJ: World Sci. Publishing, (1994), 199-209.
  • Wang, Y., Liu, X., On φ-recurrent almost Kenmotsu manifolds, Kuwait J. Sci., 42 (2015), 65-77.
  • Wang, Y., Liu, X., On a type of almost Kenmotsu manifolds with harmonic curvature tensors, Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), 15-24.
  • Wang, Y., Cotton tensor on almost cokähler 3-manifolds, Ann. Polon. Math., 120(2) (2017).
  • Zhen, G., Cabrerizo, J. L., Fernández, L.M., Fernández, M., On ξ-conformally flat contact metric manifolds, Indian J. Pure Appl. Math., 28 (1997), 725-734.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Dibakar Dey 0000-0001-8992-6501

Pradip Majhi 0000-0002-4364-1815

Project Number 09/028(1010)/2017-EMR-1
Publication Date June 30, 2021
Submission Date March 6, 2020
Acceptance Date November 8, 2020
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Dey, D., & Majhi, P. (2021). A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 52-63. https://doi.org/10.31801/cfsuasmas.699780
AMA Dey D, Majhi P. A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):52-63. doi:10.31801/cfsuasmas.699780
Chicago Dey, Dibakar, and Pradip Majhi. “A Classification of $(k,\mu)’$-Almost Kenmotsu Manifolds Admitting Cotton Tensor”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 52-63. https://doi.org/10.31801/cfsuasmas.699780.
EndNote Dey D, Majhi P (June 1, 2021) A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 52–63.
IEEE D. Dey and P. Majhi, “A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 52–63, 2021, doi: 10.31801/cfsuasmas.699780.
ISNAD Dey, Dibakar - Majhi, Pradip. “A Classification of $(k,\mu)’$-Almost Kenmotsu Manifolds Admitting Cotton Tensor”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 52-63. https://doi.org/10.31801/cfsuasmas.699780.
JAMA Dey D, Majhi P. A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:52–63.
MLA Dey, Dibakar and Pradip Majhi. “A Classification of $(k,\mu)’$-Almost Kenmotsu Manifolds Admitting Cotton Tensor”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 52-63, doi:10.31801/cfsuasmas.699780.
Vancouver Dey D, Majhi P. A classification of $(k,\mu)’$-almost Kenmotsu manifolds admitting Cotton tensor. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):52-63.

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

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