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In index-free notation it is defined as =, where is the Ricci tensor, is the metric tensor and is the scalar curvature, which is computed as the trace of the Ricci tensor by = . In component form, the previous equation reads as G μ ν = R μ ν − 1 2 g μ ν R . {\displaystyle G_{\mu \nu }=R_{\mu \nu }-{1 \over 2}g_{\mu \nu }R.}
The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...
The kappa curve has two vertical asymptotes. In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter ϰ (kappa).The kappa curve was first studied by Gérard van Gutschoven around 1662.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
The first Frenet-Serret formula holds by the definition of the normal N and the curvature κ, and the third Frenet-Serret formula holds by the definition of the torsion τ. Thus what is needed is to show the second Frenet-Serret formula. Since T, N, B are orthogonal unit vectors with B = T × N, one also has T = N × B and N = B × T.
In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [1] [2] [3]
The FIA Formula 2 Championship [1] is a second-tier single-seater championship organized by the Fédération Internationale de l'Automobile (FIA). Held on racing circuits, the championship was introduced in 2017, following the rebranding of the long-term Formula One feeder series GP2.
In February 2017, live streaming was introduced to the official YouTube mobile app. Live streaming via mobile was initially restricted to users with at least 10,000 subscribers, [67] but as of mid-2017 it has been reduced to 100 subscribers. [68] Live streams support HDR, can be up to 4K resolution at 60 fps, and also support 360° video. [49] [69]