the christoffel symbols
41Einstein's constant — or Einstein s gravitational constant, noted kappa; (kappa), is the coupling constant appearing in the Einstein field equation which can be written: G^{alpha gamma} = kappa , T^{alpha gamma} where Gα gamma; is the Einstein tensor and Tα gamma; is… …
42Riemann curvature tensor — In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor is the most standard way to express curvature of Riemannian manifolds. It is one of many things named after Bernhard Riemann and Elwin… …
43Levi-Civita connection — In Riemannian geometry, the Levi Civita connection is the torsion free Riemannian connection, i.e., the torsion free connection on the tangent bundle (an affine connection) preserving a given (pseudo )Riemannian metric.The fundamental theorem of… …
44Laplace operator — This article is about the mathematical operator. For the Laplace probability distribution, see Laplace distribution. For graph theoretical notion, see Laplacian matrix. Del Squared redirects here. For other uses, see Del Squared (disambiguation) …
45Ricci curvature — In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci Curbastro, provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n… …
46Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …
47Weyl tensor — In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal… …
48Laplace-Beltrami operator — In differential geometry, the Laplace operator can be generalized to operate on functions defined on surfaces, or more generally on Riemannian and pseudo Riemannian manifolds. This more general operator goes by the name Laplace Beltrami operator …
49Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …
50Newtonian dynamics — In physics, the Newtonian dynamics is understood as the dynamics of a particle or a small body according to Newton s laws of motion. Contents 1 Mathematical generalizations 2 Newton s second law in a multidimensional space 3 Euclidean structure …
