The terms elliptic, hyperbolic and euclidean geometry are defined according to the sectional curvature, which is a generalization of the Gaussian curvature of a surface. Are there any restrictions on the sectional curvature for spacetimes in general relativity?(adsbygoogle = window.adsbygoogle || []).push({});

The Ricci scalar, being a function of the trace of the energy-momentum tensor [tex]R = - \kappa T^{\alpha}_{\alpha}[/tex], must be always positive? Can be the sectional curvature defined as a function of the Ricci scalar?

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# Sectional curvature in GR

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