Conharmonic curvature tensor and the spacetime of general relativity.

*(English)*Zbl 1202.83015Summary: 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 | Lorentz manifolds, manifolds with indefinite metrics |

53C80 | Applications of global differential geometry to physics |

83E05 | Geometrodynamics |

53B35 | Hermitian and Kählerian structures (local differential geometry) |

83F05 | Relativistic cosmology |

83C55 | Macroscopic interaction of the gravitational field with matter (general relativity) |