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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

  • Connection (principal bundle) — This article is about connections on principal bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way …   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

  • Ehresmann 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… …   Wikipedia

  • Seiberg–Witten invariant — In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4 manifolds introduced by harvtxt|Witten|1994, using the Seiberg Witten theory studied by harvs|txt=yes|last=Seiberg|last2=Witten|year1=1994a|year2=1994b during their… …   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

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Gauge theory — For a generally accessible and less technical introduction to the topic, see Introduction to gauge theory. In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations …   Wikipedia

  • Mass–energy equivalence — E=MC2 redirects here. For other uses, see E=MC2 (disambiguation). 4 meter tall sculpture of Einstein s 1905 E = mc2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the …   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

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