High Quality Content by WIKIPEDIA articles! In the theory of general relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only geodesics. The method is named for Alfred Schild, who introduced the method during lectures at Princeton University. The idea is to identify a tangent vector x at a point A0 with a geodesic segment of unit length A0X0, and to construct an approximate...
High Quality Content by WIKIPEDIA articles! In the theory of general relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only geodesics. The method is named for Alfred Schild, who introduced the method during lectures at Princeton University. The idea is to identify a tangent vector x at a point A0 with a geodesic segment of unit length A0X0, and to construct an approximate parallelogram with approximately parallel sides A0X0 and A1X1 as an approximation of the Levi-Civita parallelogramoid; the new segment A1X1 thus corresponds an approximately parallel translated tangent vector at A1.
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