Vol.3, No 14, 2003 pp. 843-849
UDC 514.82
Invited Paper

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ON A PERFECT FLUID SPACE-TIME ADMITTING
QUASI CONFORMAL CURVATURE TENSOR
Sarbari Guha
Dept. of Physics, St. Xavier's College, 30 Park Street, Kolkata 700 016
E-mail: sarbariguha@ rediffmail.com

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Abstract. The notion of the quasi conformal curvature tensor C* of type (1,3) in a Riemannian manifold (Mn,g) (n>3) was introduced by M. C. Chaki and M. L. Ghosh [1] according to whom
C*(X,Y,Z) = aR(X,Y,Z) + b[S(Y,Z)X ? S(X,Z)Y + g(Y,Z)QX – g(X,Z)QY]
?  [  + 2b][g(Y,Z)X –g(X,Z)Y]
where a and b are  constants, R is the Riemann tensor of type (1,3), S is the Ricci tensor of type (0,2), Q is the Ricci tensor of type (1,1) and r is the scalar curvature of the manifold.
In this paper, a four-dimensional perfect fluid space-time with a Lorentz metric of signature (+,+,+,?) and non-zero scalar curvature, admitting a quasi conformal curvature tensor ,has been considered.
It is shown that, if such a fluid space-time with unit timelike velocity vector field obeys Einstein's equation with cosmological constant and its quasi conformal curvature tensor is divergence-free then the fluid is shear-free, irrotational and its energy density is constant over the hypersurface orthogonal to the velocity vector field.

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O PROSTOR-VREMENU, KOJI DOZVOLJAVA
KVAZI-KONFORMNI TENZOR KRIVINE,
I PREDSTAVLJA IDEALNI FLUID Pojam kvazi-konformalnog tezora krivina C* tipa (1,3) na Riemannian višestrukosti (M*,g) (n>3) su uveli M.C.Chaki i M.L.Ghash [1] u saglasnosti sa:
C*(X,Y,Z) = aR(X,Y,Z) + b[S(Y,Z)X ? S(X,Z)Y + g(Y,Z)QX – g(X,Z)QY]
?  [  + 2b][g(Y,Z)X –g(X,Z)Y]
gde su gde su  konstante, R Reimann-ov tenzor tipa (1,3), S je Ricci-jev tenzor tipa (0,2),  Q  je Ricci-jev tenzor tipa (1,1), i r je skalar krivine mnogostrukosti.
U ovom  radu, četvoro-dimenzionalni prostor-vreme, koji predstavlja idealni fluid,  sa Lorentz-ovom metrikom  signature (+,+,+, -) i ne nultom skalarnom krivinom, koji  dozvoljava kvazikonformni tenzor krivine,  je razmotren. Pokazano je daako takav  prostor vreme, koji predstavlja fluid, sa jediničnim vremeski sličnim vektorskim poljem brzine zadovoljava Einstein-ovu jednačinu sa kosmološkom konstantom i njegov kvazi-konformni tenzor krivine je bez divergencije, tada je fluid slobodno- smičući, nerotirajući i njegova gustina energije je konstantna nad hiperprostorom ortogonalnim vektorsko polje brzina.