Browse > Article
http://dx.doi.org/10.5666/KMJ.2020.60.1.185

The 𝒲⁎-curvature Tensor on Relativistic Space-times  

Abu-Donia, Hassan (Department of Mathematics, Faculty of Science, Zagazig University)
Shenawy, Sameh (Basic Science Department, Modern Academy for Engineering and Technology)
Syied, Abdallah Abdelhameed (Department of Mathematics, Faculty of Science, Zagazig University)
Publication Information
Kyungpook Mathematical Journal / v.60, no.1, 2020 , pp. 185-195 More about this Journal
Abstract
This paper aims to study the 𝒲⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲⁎-curvature tensor is Einstein. A 𝒲⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲⋆-curvature tensor are considered.
Keywords
Einstein's field equation; perfect fluid space-times; energy-momentum tensor; semi-symmetric curvature tensor;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Z. Ahsan and M. Ali, Curvature tensor for the spacetime of general relativity, Int. J. Geom. Methods Mod. Phys., 14(5)(2017), 1750078, 13 pp.   DOI
2 U. C. De and L. Velimirovic , Spacetimes with semisymmetric energy-momentum tensor, Internat. J. Theoret. Phys., 54(6)(2015), 1779-1783.   DOI
3 D. Krupka, The trace decomposition of tensors of type (1,2) and (1,3), New Developments in Differential Geometry, 243-253, Math. Appl. 350, Kluwer Acad. Publ., Dordrecht, 1996.
4 S. Mallick and U. C. De, Space-times admitting $W_2$-curvature tensor, Int. J. Geom. Methods Mod. Phys., 11(4)(2014), 1450030, 8 pp.   DOI
5 S. Mallick, Y. J. Suh and U. C. De, A spacetime with pseudo-projective curvature tensor, J. Math. Phys., 57(2016), 062501, 10 pp.   DOI
6 C. A. Mantica and Y. J. Suh, Pseudo Z symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys., 9(1)(2012), 1250004, 21 pp.   DOI
7 C. A. Mantica and Y. J. Suh, Pseudo Z Symmetric Space-times, J. Math. Phys., 55(2014), 042502, 12 pp.   DOI
8 V. A. Mirzoyan, Ricci semisymmetric submanifolds(Russian), Itogi Nauki i Tekhniki: Problemy Geometrii 23, pp. 29-66, VINITI, Moscow, 1991.
9 B. O'Neill, Semi-Riemannian geometry, Academic Press, New York, 1983.
10 R. S. Mishra, Structures on differentiable manifold and their applications, Chandrama Prakasana, Allahabad, 1984.
11 F. Ozen Zengin, On Riemannian manifolds admitting $W_2$-curvature tensor, Miskolc Math. Notes, 12(2011), 289-296.   DOI
12 G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance, Yokohama Math. J., 18(1970), 105-108.
13 G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance II, Yokohama Math. J., 19(1971), 97-103.
14 G. P. Pokhariyal, Curvature tensor and their relativistic significance III, Yokohama Math. J., 20(1972), 115-119.
15 G. P. Pokhariyal, Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci., 5(1982), 133-139.   DOI
16 G. P. Pokhariyal, Curvature tensors on A-Einstein Sasakian manifolds, Balkan J. Geom. Appl., 6(2001), 45-50.
17 R. K. Sach and W. Hu, General relativity for mathematician, Springer Verlag, New York, 1977.
18 S. Shenawy and Bulent Unal, The $W_2$-curvature tensor on warped product manifolds and applications, Int. J. Geom. Methods Mod. Phys., 13(7)(2016), 1650099, 14 pp.   DOI
19 Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y)${\cdot}$R = 0 I, J. Diff. Geom., 17(1982), 531-582.   DOI
20 A. Taleshian and A. A. Hosseinzadeh, On $W_2$-curvature tensor of N(k)-quasi-Einstein manifolds, J. Math. Comput. Sci., 1(1)(2010), 28-32.   DOI