the christoffel symbols
21Greek letters used in mathematics, science, and engineering — Greek alphabet Αα Alpha Νν Nu Ββ Beta …
22Manifest covariance — In general relativity, an equation is said to be manifestly covariant if all expressions in the equation are tensors. The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant… …
23Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… …
24Gaussian curvature — In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ 1 and κ 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how… …
25Conformal geometry — In mathematics, conformal geometry is the study of the set of angle preserving (conformal) transformations on a space. In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces. In more than two dimensions,… …
26Hessian matrix — In mathematics, the Hessian matrix (or simply the Hessian) is the square matrix of second order partial derivatives of a function; that is, it describes the local curvature of a function of many variables. The Hessian matrix was developed in the… …
27Metric tensor (general relativity) — This article is about metrics in general relativity. For a discussion of metrics in general, see metric tensor. Metric tensor of spacetime in general relativity written as a matrix. In general relativity, the metric tensor (or simply, the metric) …
28Linearized gravity — is an approximation scheme in general relativity in which the nonlinear contributions from the spacetime metric are ignored. This allows the study of many problems to be simplified. The methodIn linearized gravity, the metric tensor of spacetime… …
29Stress-energy-momentum pseudotensor — In the theory of general relativity, a stress energy momentum pseudotensor, such as the Landau Lifshitz pseudotensor, is an extension of the non gravitational stress energy tensor which incorporates the energy momentum of gravity. It allows the… …
30Ehresmann connection — In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of the notion of a connection which is defined on arbitrary fibre bundles. In particular, it may… …
