## Investigation of some conditions on $$N(k)$$-quasi Einstein manifolds.(English)Zbl 1232.53041

A locally-symmetric type condition but with the usual curvature tensor field replaced by other curvature fields (conharmonic, projective and pseudo-projective) is analyzed in $$N(k)$$-quasi Einstein geometry. Although two examples of perfect fluid space-times are presented at the beginning, the above geometrical conditions and their possible (physical) consequences are not discussed for these examples.
$$N(k)$$-quasi Einstein manifold