Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
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TL;DR: In this article, the Bianchi type I model with perfect fluid as matter content in f(R,T) gravity was discussed, where R is the Ricci scalar and T is the trace of the energy-momentum tensor.
Abstract: We discuss the Bianchi type I model with perfect fluid as matter content in f(R,T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. We obtain exact solutions of the field equations employing the anisotropic feature of spacetime for two expansion laws namely exponential and power expansions. The physical and kinematical quantities are examined for both cases in future evolution of the universe. We also explore the validity of null energy condition and conclude that our solutions are consistent with the current observations.
71 citations
TL;DR: In this paper, the conditions for existence of maximally symmetric N-dimensional De Sitter space-times in gravity theories derived from the variation of an action containg a lagrangian which is an arbitrary analytic function of the quadratic curvature invariants formed from the scalar, Ricci, and Riemann curvatures.
71 citations
71 citations
71 citations
01 Jan 1993
TL;DR: The Petersson-Weil metric is a main tool for investigating the geometry of moduli spaces, and it was shown by Wolpert and Tromba in 1986 that the Ricci curvature is negative as mentioned in this paper.
Abstract: The Petersson-Weil metric is a main tool for investigating the geometry of moduli spaces. When A. Weil considered the classical Teichmuller space from the viewpoint of deformation theory, he suggested, in 1958, investigating the Petersson inner product on the space of holomorphic quadratic differentials. He conjectured that it induced a Kahler metric on the Teichmuller space. After proving this property, Ahlfors showed, in 1961, that the holomorphic sectional and Ricci curvatures were negative. Royden’s conjecture of a precise upper bound for the holomorphic sectional curvature was proven by Wolpert and Tromba in 1986 along with the negativity of the sectional curvature.
71 citations