Siddiqui, Shah Alam; Ahsan, Zafar Conharmonic curvature tensor and the spacetime of general relativity. (English) Zbl 1202.83015 Differ. Geom. Dyn. Syst. 12, 213-220 (2010). Summary: The significance of the conharmonic curvature tensor is very well known in the differential geometry of certain \(F\)-structures (e.g., complex, almost complex, Kähler, almost Kähler, Hermitian, almost Hermitian structures, etc.). In this paper, a study of the conharmonic curvature tensor has been made on the four dimensional space-time of general relativity.The space-time satisfying Einstein’s field equations and having vanishing conharmonic tensor is considered and the existence of Killing and conformal Killing vectors on such space-time have been established. Perfect fluid cosmological models have also been studied. Cited in 17 Documents MSC: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C80 Applications of global differential geometry to the sciences 83E05 Geometrodynamics and the holographic principle 53B35 Local differential geometry of Hermitian and Kählerian structures 83F05 Relativistic cosmology 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) Keywords:conharmonic curvature tensor; Killing and conformal Killing vectors; perfect fluid spacetime PDFBibTeX XMLCite \textit{S. A. Siddiqui} and \textit{Z. Ahsan}, Differ. Geom. Dyn. Syst. 12, 213--220 (2010; Zbl 1202.83015)