On Riemannian manifolds admitting $W_2$-curvature tensor

Füsun Özen Zengin
2011 Miskolc Mathematical Notes  
The object of this paper is to study the properties of flat spacetimes under some conditions regarding the W 2 -curvature tensor. In the first section, several results are obtained on the geometrical symmetries of this curvature tensor. It is shown that in a spacetime with W 2curvature tensor filled with a perfect fluid, the energy momentum tensor satisfying the Einstein's equations with a cosmological constant is a quadratic conformal Killing tensor. It is also proved that a necessary and
more » ... necessary and sufficient condition for the energy momentum tensor to be a quadratic Killing tensor is that the scalar curvature of this space must be constant. In a radiative perfect fluid, it is shown that the sectional curvature is constant.
doi:10.18514/mmn.2011.332 fatcat:ii437krj7zbyhix4cfkkj7fiui