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Conharmonic curvature tensor and the spacetime of general relativity. (English) Zbl 1202.83015

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:

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.)
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