Research Article
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Year 2022, , 39 - 46, 30.04.2022

Ayşe Yavuz Taşcı , Füsun Özen

https://doi.org/10.36890/iejg.986956
Cited By: 2

Abstract

References

  • [1] Mishra, R. S.: Structures on a differentiable manifold and their applications. Chandrama Prakasana. Allahabad, India (1984).
  • [2] Shaikh, A. A., Hui, S. K.: On weakly projective symmetric manifolds. Acta Math. Acad. Paedagog. Nyhazi (N.S.) 25 (2), 247-269 (2009).
  • [3] Chaki, M. C., Saha, S. K.: On pseudo-projective Ricci symmetric manifolds. Bulgar. J. Phys. 21, 1-7 (1994).
  • [4] Yano, K., Bochner, S.: Curvature and Betti Numbers. Princeton University Press. (1953).
  • [5] Mikesh, J.: Differential Geometry of Special Mappings. Palacky University, Faculty of Science. Olomouc (2015).
  • [6] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces. Nauka, Moscow (1979).
  • [7] Szabo, Z. I.: Structure theorems on Riemannian spaces satisfying R(X,Y).R = 0 J. Diff. Geom. 17, 531–582 (1982).
  • [8] Shaikh, A. A., Kundu, H.: On equivalency of various geometric structures J. Geom. 105, 139–165 (2014).
  • [9] De, U. C., Sarkar, A.: On the projective curvature tensor of generalized Sasakianspace-forms Quaest. Math. 33 (2), 245–252 (2010).
  • [10] Satyanarayana, T., Prasad, K. L. S.: On Semi-symmetric Para Kenmotsu Manifolds Turkish J. Anal. Number Theo. 3 (6), 145–148 (2015).
  • [11] Shaikh, A. A., Baishya, K. K.: On (k;μ)-contact metric manifolds An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) LI (2), 405–416 (2005).
  • [12] Deprez, J., Roter, W., Verstraelen, L.: Conditions on the projective curvature tensor of conformally flat Riemannian manifolds Kyungpook Math.J. 29 (2), 153-166 (1989).
  • [13] Petrovic-Torgasev, M., Verstraelen, L.: On the concircular curvature tensor, the projective curvature tensor and the Einstein curvature tensor of Bochner–Kaehler manifolds Math. Rep. Toyama Univ. 10, 37-61 (1987).
  • [14] Gray, A.: Einstein-like manifolds which are not Einstein Geom. Dedicata 7, 259-280 (1978).
  • [15] De, U. C., Guha, N., Kamilya, D.: On generalized Ricci-recurrent manifolds Tensor(NS) 56, 312-317 (1995).
  • [16] Ruse, H.S.: Three-Dimensional Spaces of Recurrent Curvature Proc. Lond. Math. Soc. 50, 438-446 (1949).
  • [17] Chaki, M.C.: Some theorems on recurrent and Ricci-recurrent spaces Rendiconti del Seminario Matematico della Universita di Padova 26, 168-176 (1956).
  • [18] Prakash, N.: A note on Ricci-recurrent and recurrent spaces Bull. Calcutta Math. Soc. 54, 1-7 (1962).
  • [19] Yamaguchi, S., Matsumoto, M.: On Ricci-recurrent spaces Tensor (N.S) 19, 64-68 (1968).
  • [20] Mantica, C.A., Molinari, L.G.: Weakly Z-symmetric manifold Acta Math. Hungar. 135, 80-96 (2012).
  • [21] Besse, A. L.: Einstein Manifolds. Springer-Verlag, Berlin Heidelberg (1987).
  • [22] De, U. C., Guha, N., Kamilya, D.: On generalized Ricci-recurrent manifolds Tensor (N.S) 56, 312-317 (1995).
  • [23] Derdzinski, A., Shen, C.L.: Codazzi tensor fields, curvature and Pontryagin forms Proc. Lond. Math. Soc. 47, 15-26 (1983).
  • [24] Roter, W.: On a generalization of conformally symmetric metrics Tensor (NS) 46, 278-286 (1987).
  • [25] de Felice, F., Clarke, C. J. S.: Relativity on curved manifolds. Cambridge University Press. (1990).
  • [26] De, U. C., Mantica, C. A., Suh, Y. J.: On weakly cyclic Z symmetric manifolds Acta Math. Hungar. 146 (1), 153-167 (2015).
  • [27] Mantica, C. A., Suh, Y. J.: Pseudo Z symmetric riemannian manifolds with harmonic curvature tensors Int. J. Geom. Meth. Mod. Phys. 9 (1), 1250004 1–21 (2012).
  • [28] Mantica, C. A., Suh, Y. J.: Pseudo-Z symmetric spacetimes J. Math. Phys. 55 (4), 042502, 12pp (2014).
  • [29] Mantica, C.A., Suh, Y. J.: Recurrent Z forms on Riemannian and Kaehler manifolds Int. J. Geom. Meth. Mod. Phys. 9 (7), 1250059 1-26 (2012).
  • [30] De, U. C., Pal, P.: On almost pseudo-Z-symmetric manifolds Acta Univ. Palacki., Fac. rer. nat., Mathematica 53 (1), 25-43 (2014).
  • [31] De, U. C.: On weakly Z symmetric spacetimes Kyungpook Math. J. 58, 761-779 (2018).
  • [32] Yavuz Taşcı, A., Özen Zengin, F.: Concircularly flat Z-symmetric manifolds An. Stiint. Univ. Al. I. Cuza Iasi TomLXV (2), 241-250 (2019).
  • [33] Yavuz Taşcı, A., Özen Zengin, F.: Z-symmetric manifold admitting concircular Ricci symmetric tensor Afrika Matematika 31, 1093-1104 (2020).

On Z-Symmetric Manifold Admitting Projective Curvature Tensor

Year 2022, , 39 - 46, 30.04.2022

Ayşe Yavuz Taşcı , Füsun Özen

https://doi.org/10.36890/iejg.986956
Cited By: 2

Abstract

The object of the present paper is to study the Z-symmetric manifold with the projective curvature tensor.
At first, we study the case of Z-tensor and projective Ricci tensor being of Codazzi type. Next, we consider recurrent Z-tensor and recurrent projective Ricci tensor. We also study the Z-symmetric manifold with projective curvature tensor with divergence-free Z-tensor. Finally, we construct an example of the Z-symmetric manifold with projective curvature tensor.

Keywords

Projective curvature tensor Z-symmetric tensor Codazzi tensor recurrent tensor

References

  • [1] Mishra, R. S.: Structures on a differentiable manifold and their applications. Chandrama Prakasana. Allahabad, India (1984).
  • [2] Shaikh, A. A., Hui, S. K.: On weakly projective symmetric manifolds. Acta Math. Acad. Paedagog. Nyhazi (N.S.) 25 (2), 247-269 (2009).
  • [3] Chaki, M. C., Saha, S. K.: On pseudo-projective Ricci symmetric manifolds. Bulgar. J. Phys. 21, 1-7 (1994).
  • [4] Yano, K., Bochner, S.: Curvature and Betti Numbers. Princeton University Press. (1953).
  • [5] Mikesh, J.: Differential Geometry of Special Mappings. Palacky University, Faculty of Science. Olomouc (2015).
  • [6] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces. Nauka, Moscow (1979).
  • [7] Szabo, Z. I.: Structure theorems on Riemannian spaces satisfying R(X,Y).R = 0 J. Diff. Geom. 17, 531–582 (1982).
  • [8] Shaikh, A. A., Kundu, H.: On equivalency of various geometric structures J. Geom. 105, 139–165 (2014).
  • [9] De, U. C., Sarkar, A.: On the projective curvature tensor of generalized Sasakianspace-forms Quaest. Math. 33 (2), 245–252 (2010).
  • [10] Satyanarayana, T., Prasad, K. L. S.: On Semi-symmetric Para Kenmotsu Manifolds Turkish J. Anal. Number Theo. 3 (6), 145–148 (2015).
  • [11] Shaikh, A. A., Baishya, K. K.: On (k;μ)-contact metric manifolds An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) LI (2), 405–416 (2005).
  • [12] Deprez, J., Roter, W., Verstraelen, L.: Conditions on the projective curvature tensor of conformally flat Riemannian manifolds Kyungpook Math.J. 29 (2), 153-166 (1989).
  • [13] Petrovic-Torgasev, M., Verstraelen, L.: On the concircular curvature tensor, the projective curvature tensor and the Einstein curvature tensor of Bochner–Kaehler manifolds Math. Rep. Toyama Univ. 10, 37-61 (1987).
  • [14] Gray, A.: Einstein-like manifolds which are not Einstein Geom. Dedicata 7, 259-280 (1978).
  • [15] De, U. C., Guha, N., Kamilya, D.: On generalized Ricci-recurrent manifolds Tensor(NS) 56, 312-317 (1995).
  • [16] Ruse, H.S.: Three-Dimensional Spaces of Recurrent Curvature Proc. Lond. Math. Soc. 50, 438-446 (1949).
  • [17] Chaki, M.C.: Some theorems on recurrent and Ricci-recurrent spaces Rendiconti del Seminario Matematico della Universita di Padova 26, 168-176 (1956).
  • [18] Prakash, N.: A note on Ricci-recurrent and recurrent spaces Bull. Calcutta Math. Soc. 54, 1-7 (1962).
  • [19] Yamaguchi, S., Matsumoto, M.: On Ricci-recurrent spaces Tensor (N.S) 19, 64-68 (1968).
  • [20] Mantica, C.A., Molinari, L.G.: Weakly Z-symmetric manifold Acta Math. Hungar. 135, 80-96 (2012).
  • [21] Besse, A. L.: Einstein Manifolds. Springer-Verlag, Berlin Heidelberg (1987).
  • [22] De, U. C., Guha, N., Kamilya, D.: On generalized Ricci-recurrent manifolds Tensor (N.S) 56, 312-317 (1995).
  • [23] Derdzinski, A., Shen, C.L.: Codazzi tensor fields, curvature and Pontryagin forms Proc. Lond. Math. Soc. 47, 15-26 (1983).
  • [24] Roter, W.: On a generalization of conformally symmetric metrics Tensor (NS) 46, 278-286 (1987).
  • [25] de Felice, F., Clarke, C. J. S.: Relativity on curved manifolds. Cambridge University Press. (1990).
  • [26] De, U. C., Mantica, C. A., Suh, Y. J.: On weakly cyclic Z symmetric manifolds Acta Math. Hungar. 146 (1), 153-167 (2015).
  • [27] Mantica, C. A., Suh, Y. J.: Pseudo Z symmetric riemannian manifolds with harmonic curvature tensors Int. J. Geom. Meth. Mod. Phys. 9 (1), 1250004 1–21 (2012).
  • [28] Mantica, C. A., Suh, Y. J.: Pseudo-Z symmetric spacetimes J. Math. Phys. 55 (4), 042502, 12pp (2014).
  • [29] Mantica, C.A., Suh, Y. J.: Recurrent Z forms on Riemannian and Kaehler manifolds Int. J. Geom. Meth. Mod. Phys. 9 (7), 1250059 1-26 (2012).
  • [30] De, U. C., Pal, P.: On almost pseudo-Z-symmetric manifolds Acta Univ. Palacki., Fac. rer. nat., Mathematica 53 (1), 25-43 (2014).
  • [31] De, U. C.: On weakly Z symmetric spacetimes Kyungpook Math. J. 58, 761-779 (2018).
  • [32] Yavuz Taşcı, A., Özen Zengin, F.: Concircularly flat Z-symmetric manifolds An. Stiint. Univ. Al. I. Cuza Iasi TomLXV (2), 241-250 (2019).
  • [33] Yavuz Taşcı, A., Özen Zengin, F.: Z-symmetric manifold admitting concircular Ricci symmetric tensor Afrika Matematika 31, 1093-1104 (2020).
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ayşe Yavuz Taşcı 0000-0003-2939-3330

Füsun Özen 0000-0002-5468-5100

Publication Date April 30, 2022
Acceptance Date November 26, 2021
Published in Issue Year 2022

Cite

APA Yavuz Taşcı, A., & Özen, F. (2022). On Z-Symmetric Manifold Admitting Projective Curvature Tensor. International Electronic Journal of Geometry, 15(1), 39-46. https://doi.org/10.36890/iejg.986956
AMA Yavuz Taşcı A, Özen F. On Z-Symmetric Manifold Admitting Projective Curvature Tensor. Int. Electron. J. Geom. April 2022;15(1):39-46. doi:10.36890/iejg.986956
Chicago Yavuz Taşcı, Ayşe, and Füsun Özen. “On Z-Symmetric Manifold Admitting Projective Curvature Tensor”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 39-46. https://doi.org/10.36890/iejg.986956.
EndNote Yavuz Taşcı A, Özen F (April 1, 2022) On Z-Symmetric Manifold Admitting Projective Curvature Tensor. International Electronic Journal of Geometry 15 1 39–46.
IEEE A. Yavuz Taşcı and F. Özen, “On Z-Symmetric Manifold Admitting Projective Curvature Tensor”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 39–46, 2022, doi: 10.36890/iejg.986956.
ISNAD Yavuz Taşcı, Ayşe - Özen, Füsun. “On Z-Symmetric Manifold Admitting Projective Curvature Tensor”. International Electronic Journal of Geometry 15/1 (April 2022), 39-46. https://doi.org/10.36890/iejg.986956.
JAMA Yavuz Taşcı A, Özen F. On Z-Symmetric Manifold Admitting Projective Curvature Tensor. Int. Electron. J. Geom. 2022;15:39–46.
MLA Yavuz Taşcı, Ayşe and Füsun Özen. “On Z-Symmetric Manifold Admitting Projective Curvature Tensor”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 39-46, doi:10.36890/iejg.986956.
Vancouver Yavuz Taşcı A, Özen F. On Z-Symmetric Manifold Admitting Projective Curvature Tensor. Int. Electron. J. Geom. 2022;15(1):39-46.

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