"Espaces à connexion affine, projective et conforme", Acta Math., 48: 1–42, doi:10.1007/BF02629755 A more mathematically motivated account of affine connections...
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xv+132 pp. ISBN 3-540-09749-X Les tenseurs. Suivi de "Torseurs sur un espace affine by Y. Bamberger and J.-P. Bourguignon. Second edition. Hermann, Paris...
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point de l'espace affine attaché au point m' correspond à tel point de l'espace affine attaché au point m, que tel vecteur du premier espace es parallèle ou...
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Torsion tensor (redirect from Affine torsion)
differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors X...
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depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel...
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the affine connection and then separately posing a constraint that forces both the torsion and contorsion to be zero, which thus forces the affine connection...
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Cartan connection (section Affine connections)
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...
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geometric setting it is a statement about the triviality of vector bundles on affine space. The theorem states that every finitely generated projective module...
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quadric or a reducible quadric. A quadric is an affine algebraic variety, or, if it is reducible, an affine algebraic set. Quadrics may also be defined in...
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category theory used in multiple contexts, such as with covering spaces (espace étalé). They were introduced as a mechanism for keeping track of data surrounding...
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consisting of orthogonal unit vectors (an orthonormal basis). An affine frame of an affine space consists of a choice of origin along with an ordered basis...
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Solder form (section Affine bundles and vector bundles)
structure group. Ehresmann, C. (1950). "Les connexions infinitésimales dans un espace fibré différentiel". Colloque de Topologie, Bruxelles: 29–55. Kobayashi...
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and in particular semisimple Lie algebras. There is a generalization to affine Lie algebras shown by Feigin and Frenkel showing that an algebra known as...
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the weak topology, then every group (or equivalently: every semigroup) of affine isometries of K {\displaystyle K} has at least one fixed point. (Here, a...
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Alain Connes and André Lichnerowicz, Paris, O. Jacob; Saint-Gély du Fesc : Espace 34 (2000)/Triangle of thoughts Les failles du darwinisme, La Recherche,...
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regarded as affine symmetric spaces. If M = G / H is a symmetric space, then Nomizu showed that there is a G-invariant torsion-free affine connection (i...
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espaces fibrés différentiables". Comptes rendus de l'Académie des Sciences. 224: 1611–1612. Ehresmann, Charles (1955). "Les prolongements d'un espace...
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supremum of coefficients), and the polydisc plays a role analogous to that of affine n-space in algebraic geometry. Points on the polydisc are defined to be...
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Euclidean lines include the affine transformations, and the symmetries of hyperbolic lines include the Möbius transformations. The affine transformations and...
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Connection. His subsequent research involved using intrinsically defined affine and Weylian connections to study the invariants of differential systems...
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time a discrete group acts simply transitively on the triangles in the affine Bruhat–Tits building for SL3(Qp); in 1979 Mumford discovered the first example...
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linear when applied to connections, is sometimes used (like the word affine – see Affine connection) to refer to connections defined on the tangent bundle...
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x − y ) {\displaystyle d(x,y)=p(x-y)} . This is a convex function of an affine function of x {\displaystyle x} (in particular, a translation), and therefore...
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{n}{2}}+1)^{2}}}} where Γ {\displaystyle \Gamma } is the Gamma function. By affine invariance, any ellipsoid has the same Mahler volume. The polar body of...
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de Riemann et les espaces à torsion." C. R. Acad. Sci. (Paris) 174, 593–595 (1922); Élie Cartan. "Sur les variétés à connexion affine et la théorie de...
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precisely, the space of the isomorphism classes of spin structures is an affine space over H1(M,Z2). Intuitively, for each nontrivial cycle on M a spin...
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Monde.fr (in French). 6 April 2018. Retrieved 12 April 2018. "En marche ! Espace personel". En Marche !. 2016. Archived from the original on 9 January 2017...
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allowed to have singularities. Stein spaces are the analogues of affine varieties or affine schemes in algebraic geometry. If the univalent domain on C n...
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Lebesgue covering theorem. The Lebesgue covering dimension coincides with the affine dimension of a finite simplicial complex. The covering dimension of a normal...
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homogenes dans les espaces cosmogoniques, Comptes rendus de l’Acad ́emie des Sciences, 206, 1086–1088 (in French) 1938 Les espaces des paths generalises...
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