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left invariant connection

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  • Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan …   Wikipedia

  • Cartan connection — In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the …   Wikipedia

  • Cartan connection applications — This page covers applications of the Cartan formalism. For the general concept see Cartan connection.Vierbeins, et cetera The vierbein or tetrad theory much used in theoretical physics is a special case of the application of Cartan connection in… …   Wikipedia

  • Exponential map — In differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis to all differentiable manifolds with an affine connection. Two important special cases of this are the exponential map …   Wikipedia

  • Maurer–Cartan form — In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one form on G that carries the basic infinitesimal information about the structure of G. It was much used by Élie Cartan as a basic ingredient of his method… …   Wikipedia

  • Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… …   Wikipedia

  • Geometrization conjecture — Thurston s geometrization conjecture states that compact 3 manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3 manifolds of the uniformization theorem for… …   Wikipedia

  • Anosov diffeomorphism — In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction .… …   Wikipedia

  • Relativity priority dispute — Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for… …   Wikipedia

  • Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …   Wikipedia

  • Lattice (group) — A lattice in the Euclidean plane. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn …   Wikipedia

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