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Year 2019, Volume: 7 Issue: 1, 217 - 221, 15.04.2019

Abstract

References

  • [1] Atçeken,M. and Yıldırım, U . (2016). AlmostC(a)􀀀Manifolds Satisfying Certain Curvature Conditions, Advanced Studies in ContemporaryMathematics, 26 (3), 567-578.
  • [2] Atçeken, M. and Yıldırım, U . (2016). On Almost C(a)􀀀Manifolds Satisfying Certain Conditions on Quasi-Conformal Curvature Tensor, Proceedings of the Jangjeon Mathematical Society, 19(1), 115-124.
  • [3] Chaubey, S.K. and Ojha, R.J. (2010). On the M-projecvite curvature tensor of a Kenmotsu manifold, Differential Geometry-Dynamical Systems, 12, 52-60.
  • [4] Chaubey, S.K. (2011). Some properties of LP-Sasakian manifolds equipped with M-projective curvature tensor, Bulletin of Mathematical Analysis and Applications, 3(4), 50-58.
  • [5] Chaubey, S.K., Prakash, S. and Nivas, R. (2012). Some properties of M-projective curvature tensor in Kenmotsu manifolds, Bulletin of Mathemaical Analysis and Applications, vol. 4 issue 3, 48-56.
  • [6] Devi, M.S. and Singh, J.P. (2015). On a type of M-projective curvature tensor in Kenmotsu manifolds, International J. of Math. Sci.and Eng. Appl., no.III, 37-49.
  • [7] Kenayuki, S. and Williams, F.L. (1985). Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. vol. 99, 173-187.
  • [8] Kumar, R. (2016). M-projective curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, International Journal of Mathematics and its Applications, vol. 5, issue 1-A, 81-91.
  • [9] Ojha, R.H. (1986). M-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math. 17(4), 481-484.
  • [10] Ojha, R.H. (1975). A note on the M-projective curvature tensor, Indian J. Pure Applied Math. 8(12), 1531-1534.
  • [11] Pokhariyal, G.P. and Mishra, R.S. (1971). Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19, 97-103.
  • [12] Singh, R.N. and Pandey, S.K. (2013). On the M-projective curvature tensor of N(k)-contact metric manifolds, ISRN Geometry, vol. 2013(2013).
  • [13] Singh, J.P. (2012). On M-projective recurrent Riemann manifold, Int. Journal of Math. Analysis, vol. 6, no. 24, 1173-1178.
  • [14] Vankatesha and Sumangala, B. (2013). On M-projective curvature tensor of a generalized Sasakian space form, Acta Math. Univ. Comenianae, vol. LXXXII, 2, 209-217.
  • [15] Welyczo, J. (2009). On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Result. Math. 54, 377-387.
  • [16] Welyczo, J. (2014). Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. MAth. 11, 965-978.
  • [17] Yano, K. and Sawaki, S. (1968). Riemannian manifolds admitting a conformal transformation group. J. Differential Geom. 2, 161–184.
  • [18] Zamkovoy, S. (2009). Canonical connections on paracontact manifolds. Ann Glob. Anal. and Geom. 36, 37-60.

A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor

Year 2019, Volume: 7 Issue: 1, 217 - 221, 15.04.2019

Abstract

In the present paper we have studied the curvature tensors of a normal paracontact metric manifold satisfying the conditions $R(\xi,Y)W^{*}=0$, $W^{*}(\xi,Y)R=0$, $W^{*}(\xi,Y)\widetilde{Z}=0$, $W^{*}(\xi,Y)S=0$ and $W^{*}(\xi,Y)\widetilde{C}=0$, where $W^{*}$,$R$, $S$, $\widetilde{Z}$ and $\widetilde{C}$ are the $M$-projective curvature, Riemannian curvature, Ricci, concircular curvature and quasi-conformal curvature tensor, respectively.

References

  • [1] Atçeken,M. and Yıldırım, U . (2016). AlmostC(a)􀀀Manifolds Satisfying Certain Curvature Conditions, Advanced Studies in ContemporaryMathematics, 26 (3), 567-578.
  • [2] Atçeken, M. and Yıldırım, U . (2016). On Almost C(a)􀀀Manifolds Satisfying Certain Conditions on Quasi-Conformal Curvature Tensor, Proceedings of the Jangjeon Mathematical Society, 19(1), 115-124.
  • [3] Chaubey, S.K. and Ojha, R.J. (2010). On the M-projecvite curvature tensor of a Kenmotsu manifold, Differential Geometry-Dynamical Systems, 12, 52-60.
  • [4] Chaubey, S.K. (2011). Some properties of LP-Sasakian manifolds equipped with M-projective curvature tensor, Bulletin of Mathematical Analysis and Applications, 3(4), 50-58.
  • [5] Chaubey, S.K., Prakash, S. and Nivas, R. (2012). Some properties of M-projective curvature tensor in Kenmotsu manifolds, Bulletin of Mathemaical Analysis and Applications, vol. 4 issue 3, 48-56.
  • [6] Devi, M.S. and Singh, J.P. (2015). On a type of M-projective curvature tensor in Kenmotsu manifolds, International J. of Math. Sci.and Eng. Appl., no.III, 37-49.
  • [7] Kenayuki, S. and Williams, F.L. (1985). Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. vol. 99, 173-187.
  • [8] Kumar, R. (2016). M-projective curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, International Journal of Mathematics and its Applications, vol. 5, issue 1-A, 81-91.
  • [9] Ojha, R.H. (1986). M-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math. 17(4), 481-484.
  • [10] Ojha, R.H. (1975). A note on the M-projective curvature tensor, Indian J. Pure Applied Math. 8(12), 1531-1534.
  • [11] Pokhariyal, G.P. and Mishra, R.S. (1971). Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19, 97-103.
  • [12] Singh, R.N. and Pandey, S.K. (2013). On the M-projective curvature tensor of N(k)-contact metric manifolds, ISRN Geometry, vol. 2013(2013).
  • [13] Singh, J.P. (2012). On M-projective recurrent Riemann manifold, Int. Journal of Math. Analysis, vol. 6, no. 24, 1173-1178.
  • [14] Vankatesha and Sumangala, B. (2013). On M-projective curvature tensor of a generalized Sasakian space form, Acta Math. Univ. Comenianae, vol. LXXXII, 2, 209-217.
  • [15] Welyczo, J. (2009). On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Result. Math. 54, 377-387.
  • [16] Welyczo, J. (2014). Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. MAth. 11, 965-978.
  • [17] Yano, K. and Sawaki, S. (1968). Riemannian manifolds admitting a conformal transformation group. J. Differential Geom. 2, 161–184.
  • [18] Zamkovoy, S. (2009). Canonical connections on paracontact manifolds. Ann Glob. Anal. and Geom. 36, 37-60.
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ümit Yıldırım

Mehmet Atçeken

Süleyman Dirik

Publication Date April 15, 2019
Submission Date June 1, 2017
Acceptance Date April 8, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Yıldırım, Ü., Atçeken, M., & Dirik, S. (2019). A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor. Konuralp Journal of Mathematics, 7(1), 217-221.
AMA Yıldırım Ü, Atçeken M, Dirik S. A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor. Konuralp J. Math. April 2019;7(1):217-221.
Chicago Yıldırım, Ümit, Mehmet Atçeken, and Süleyman Dirik. “A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 217-21.
EndNote Yıldırım Ü, Atçeken M, Dirik S (April 1, 2019) A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor. Konuralp Journal of Mathematics 7 1 217–221.
IEEE Ü. Yıldırım, M. Atçeken, and S. Dirik, “A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor”, Konuralp J. Math., vol. 7, no. 1, pp. 217–221, 2019.
ISNAD Yıldırım, Ümit et al. “A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor”. Konuralp Journal of Mathematics 7/1 (April 2019), 217-221.
JAMA Yıldırım Ü, Atçeken M, Dirik S. A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor. Konuralp J. Math. 2019;7:217–221.
MLA Yıldırım, Ümit et al. “A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 217-21.
Vancouver Yıldırım Ü, Atçeken M, Dirik S. A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor. Konuralp J. Math. 2019;7(1):217-21.
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