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Mathematical discipline which studies some properties of smooth manifolds, which allow to generalize calculus to beyond $\mathbb{R}^n$. General relativity is written in this language.

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General relativity: Induced metric and Killing vector fields

Assume that in spacetime ($M,g_{ab}$) there is a hypersurface generated by a set of independent one-parameter transformations acting on one single point, the generators of these transformations being …
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In general relativity, are light-like curves light-like geodesics?

Just as the title. If a curve is light-like, i.e. a null-curve, is it definitely a null geodesic?
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