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Zbl 1202.83015
Siddiqui, Shah Alam; Ahsan, Zafar
Conharmonic curvature tensor and the spacetime of general relativity. (English)
[J] Differ. Geom. Dyn. Syst. 12, 213-220, electronic only (2010). ISSN 1454-511X/e

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.

MSC 2000:: *83C05 Einstein's equations
53C50 Lorentz manifolds, manifolds with indefinite metrics
53C80 Appl. of global differential geometry to physics
83E05 Geometrodynamics
53B35 Complex differential geometry (local)
83F05 Relativistic cosmology
83C55 Hydrodynamics (general relativity)

Keywords: conharmonic curvature tensor; Killing and conformal Killing vectors; perfect fluid spacetime

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