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Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold

Year 2019, Volume: 68 Issue: 1, 997 - 1006, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501436

Abstract

In the present paper we have studied the curvature tensor of a normal paracontact metric manifold satisfying the conditions R(ξ,X)P=0, P(ξ,X)R=0, P(ξ,X)P=0, P(ξ,X)S=0, P(ξ,X)Z=0 and pseudo projective flatness, where R, P, S and Z denote the Riemannian curvature, pseudo projective curvature, Ricci and concircular curvature tensors, respectively.

References

  • Acet, B.E., Kılıç E. and Yüksel Perktaş, S., Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, International Journal of Mathematics and Mathematical Sciences, Volume 2012, (2012) Article ID 395462, 24 pages.
  • Acet, B.E. and Yüksel Perktaş, S., On para-Sasakian manifolds with a canonical paracontact connection, New Trends in Math. Sci. 4, No. 3, 162-173.
  • Prasad, B., A pseudo projective curvature tensor on a Riemannian manifold. Bull. Calcutta Math. Soc., 94, (2002), 163-166.
  • Narain, D., Prakash, A. and Prasad, B., A pseudo projective curvature tensor on a Lorentzian para-Sasakian manifold. Analele Stııntıfıce Ale Unıversıtatıı "AlI.Cuza" Dın Iası (S.N) Mathemmatica, Tomul LV, (2009). f.2.
  • Welczko, J., On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Result. Math. 54, (2009), 377-387.
  • Welczko, J., Slant curves in 3-dimensional normal paracontact metric manifolds. Mediterr. J. Math. 11, (2014), 965-978.
  • Atçeken, M. and Yıldırım, Ü., Almost C(α)-Manifolds Satisfying Certain Curvature Conditions. Advanced Studies in Contemporary Mathematics, 26 (3), (2016), 567-578.
  • Atçeken, M. and Yıldırım, Ü., On Almost C(α)-Manifolds Satisfying Certain Conditions on Quasi-Conformal Curvature Tensor. Proceedings of the Jangjeon Mathematical Society, 19(1), (2016), 115-124.
  • Mıshra, R. S., Structure on a differentiable manifold and their applications, Chandrama Prakashan, 50 A, Balrampur House, Allahabad, India, 1984.
  • Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds. Nagoya Math. J., Vol. 99, (1985), 173-187.
  • Zamkovoy, S., Canonical connections on paracontact manifolds. Ann Glob. Anal. Geom., 36, (2009), 37-60.
Year 2019, Volume: 68 Issue: 1, 997 - 1006, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501436

Abstract

References

  • Acet, B.E., Kılıç E. and Yüksel Perktaş, S., Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, International Journal of Mathematics and Mathematical Sciences, Volume 2012, (2012) Article ID 395462, 24 pages.
  • Acet, B.E. and Yüksel Perktaş, S., On para-Sasakian manifolds with a canonical paracontact connection, New Trends in Math. Sci. 4, No. 3, 162-173.
  • Prasad, B., A pseudo projective curvature tensor on a Riemannian manifold. Bull. Calcutta Math. Soc., 94, (2002), 163-166.
  • Narain, D., Prakash, A. and Prasad, B., A pseudo projective curvature tensor on a Lorentzian para-Sasakian manifold. Analele Stııntıfıce Ale Unıversıtatıı "AlI.Cuza" Dın Iası (S.N) Mathemmatica, Tomul LV, (2009). f.2.
  • Welczko, J., On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Result. Math. 54, (2009), 377-387.
  • Welczko, J., Slant curves in 3-dimensional normal paracontact metric manifolds. Mediterr. J. Math. 11, (2014), 965-978.
  • Atçeken, M. and Yıldırım, Ü., Almost C(α)-Manifolds Satisfying Certain Curvature Conditions. Advanced Studies in Contemporary Mathematics, 26 (3), (2016), 567-578.
  • Atçeken, M. and Yıldırım, Ü., On Almost C(α)-Manifolds Satisfying Certain Conditions on Quasi-Conformal Curvature Tensor. Proceedings of the Jangjeon Mathematical Society, 19(1), (2016), 115-124.
  • Mıshra, R. S., Structure on a differentiable manifold and their applications, Chandrama Prakashan, 50 A, Balrampur House, Allahabad, India, 1984.
  • Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds. Nagoya Math. J., Vol. 99, (1985), 173-187.
  • Zamkovoy, S., Canonical connections on paracontact manifolds. Ann Glob. Anal. Geom., 36, (2009), 37-60.
There are 11 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Ümit Yıldırım 0000-0002-7178-4223

Mehmet Atçeken 0000-0001-8665-5945

Süleyman Dirik 0000-0001-9093-1607

Publication Date February 1, 2019
Submission Date August 17, 2017
Acceptance Date June 6, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Yıldırım, Ü., Atçeken, M., & Dirik, S. (2019). Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 997-1006. https://doi.org/10.31801/cfsuasmas.501436
AMA Yıldırım Ü, Atçeken M, Dirik S. Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):997-1006. doi:10.31801/cfsuasmas.501436
Chicago Yıldırım, Ümit, Mehmet Atçeken, and Süleyman Dirik. “Pseudo Projective Curvature Tensor Satisfying Some Properties on a Normal Paracontact Metric Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 997-1006. https://doi.org/10.31801/cfsuasmas.501436.
EndNote Yıldırım Ü, Atçeken M, Dirik S (February 1, 2019) Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 997–1006.
IEEE Ü. Yıldırım, M. Atçeken, and S. Dirik, “Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 997–1006, 2019, doi: 10.31801/cfsuasmas.501436.
ISNAD Yıldırım, Ümit et al. “Pseudo Projective Curvature Tensor Satisfying Some Properties on a Normal Paracontact Metric Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 997-1006. https://doi.org/10.31801/cfsuasmas.501436.
JAMA Yıldırım Ü, Atçeken M, Dirik S. Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:997–1006.
MLA Yıldırım, Ümit et al. “Pseudo Projective Curvature Tensor Satisfying Some Properties on a Normal Paracontact Metric Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 997-1006, doi:10.31801/cfsuasmas.501436.
Vancouver Yıldırım Ü, Atçeken M, Dirik S. Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):997-1006.

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

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