- first Christoffel identity
- Математика: первое тождество Кристоффеля
Универсальный англо-русский словарь. Академик.ру. 2011.
first Christoffel identity
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Christoffel symbols/Proofs — This article contains proof of formulas in Riemannian geometry which involve the Christoffel symbols. Proof 1 Start with the Bianchi identity: R {abmn;l} + R {ablm;n} + R {abnl;m} = 0,!. Contract both sides of the above equation with a pair of… … Wikipedia
Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric … Wikipedia
List of formulas in Riemannian geometry — This is a list of formulas encountered in Riemannian geometry.Christoffel symbols, covariant derivativeIn a smooth coordinate chart, the Christoffel symbols are given by::Gamma {ij}^m=frac12 g^{km} left( frac{partial}{partial x^i} g {kj}… … Wikipedia
Riemann 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… … Wikipedia
Curvature 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… … Wikipedia
Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… … Wikipedia
Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… … Wikipedia
Introduction to mathematics of general relativity — An understanding of calculus and differential equations is necessary for the understanding of nonrelativistic physics. In order to understand special relativity one also needs an understanding of tensor calculus. To understand the general theory… … Wikipedia
Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… … Wikipedia
Maxwell's equations — For thermodynamic relations, see Maxwell relations. Electromagnetism … Wikipedia
Connection (mathematics) — In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of… … Wikipedia
