Conformal geometry studies a metric tensor only up to multiplication by a nowhere-zero positive scalar function on a real slice. A conformal class determines angles in Riemannian signature and null directions in Lorentzian signature. The complexified flat four-dimensional conformal geometry is encoded by the Klein quadric, whose incidence relation describes null separation.
Conformal geometry is a branch of differential geometry that studies geometric structures that are invariant under conformal transformations. A conformal transformation is a map between two geometric spaces that preserves angles but not necessarily lengths. This means that while the shapes of small figures are preserved up to a scaling factor, their sizes may change. In formal terms, a conformal structure on a manifold is an equivalence class of Riemannian metrics where two metrics are considered equivalent if they differ by a positive smooth function.
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