On a perfect fluid space-time admitting quasi conformal curvature tensor. (English) Zbl 1056.53022

M. C. Chaki and M. L. Ghosh [An. Stiint. Univ. Al. I. Cuza, Ser. Noua, Mat. 43, 375–381 (1997)] introduced the notion of the quasi conformal curvature tensor. A four-dimensional perfect fluid space-time with a Lorentz metric and non-zero scalar curvature, admitting a quasi conformal curvature tensor is considered. So, the authors find conditions for this fluid to be shear-free, irrotational and its energy density being constant over the hypersurface orthogonal to the velocity vector field.


53C20 Global Riemannian geometry, including pinching
83C80 Analogues of general relativity in lower dimensions
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53B30 Local differential geometry of Lorentz metrics, indefinite metrics