WebMy foremost mission in life is to restore human dignity by eliminating hunger and poverty, especially among the poor and vulnerable sectors of society: children, elderly, persons with disabilities, women, smallholder farmers, fisherfolks and urban poor communities. To do this effectively, an integrated and holistic program will have … The Christoffel symbol does not transform as a tensor, but rather as an object in the jet bundle. More precisely, the Christoffel symbols can be considered as functions on the jet bundle of the frame bundle of M, independent of any local coordinate system. See more In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a See more Under a change of variable from $${\displaystyle \left(x^{1},\,\ldots ,\,x^{n}\right)}$$ to $${\displaystyle \left({\bar {x}}^{1},\,\ldots ,\,{\bar {x}}^{n}\right)}$$, Christoffel symbols transform as where the overline … See more In general relativity The Christoffel symbols find frequent use in Einstein's theory of general relativity, where spacetime is represented by a curved 4-dimensional See more The definitions given below are valid for both Riemannian manifolds and pseudo-Riemannian manifolds, such as those of general relativity, … See more Christoffel symbols of the first kind The Christoffel symbols of the first kind can be derived either from the Christoffel symbols of the … See more Let X and Y be vector fields with components X and Y . Then the kth component of the covariant derivative of Y with respect to X is given by Here, the See more • Basic introduction to the mathematics of curved spacetime • Differentiable manifold • List of formulas in Riemannian geometry • Ricci calculus See more

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