"Espaces à connexion affine, projective et conforme", Acta Math., 48: 1–42, doi:10.1007/BF02629755 A more mathematically motivated account of affine connections...

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...

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...

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...

called the canonical form, or the tautological form. Suppose that E is an affine vector bundle (a vector bundle without a choice of zero section). Then a...

geometric setting it is a statement about the triviality of vector bundles on affine space. The theorem states that every finitely generated projective module...

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...

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...

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...

Alain Connes and André Lichnerowicz, Paris, O. Jacob; Saint-Gély du Fesc : Espace 34 (2000)/Triangle of thoughts Les failles du darwinisme, La Recherche,...

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...

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...

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...

espaces fibrés différentiables". Comptes rendus de l'Académie des Sciences. 224: 1611–1612. Ehresmann, Charles (1955). "Les prolongements d'un espace...

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...

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...

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...

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...

Euclidean lines include the affine transformations, and the symmetries of hyperbolic lines include the Möbius transformations. The affine transformations and...

{n}{2}}+1)^{2}}}} where Γ {\displaystyle \Gamma } is the Gamma function. By affine invariance, any solid ellipsoid has the same Mahler volume. The polar body...

Connection. His subsequent research involved using intrinsically defined affine and Weylian connections to study the invariants of differential systems...

2016. Nathalie Raulin; Guillaume Gendron (3 April 2017). "L'équipe Macron affine la mise en cène". Libération (in French). Retrieved 19 April 2017. Camille...

Lebesgue covering theorem. The Lebesgue covering dimension coincides with the affine dimension of a finite simplicial complex. The covering dimension of a normal...

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...

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...

characterization of Kazhdan's property (T) and of the Haagerup property using affine isometric actions on median spaces. A study of generalizations of Kazhdan's...

dissimili dal sardo, costituiscono oggi il gruppo romanzo linguisticamente più affine al sistema dei dialetti toscani." Posner, Rebecca; Sala, Marius. "Sardinian...

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...

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...

linear when applied to connections, is sometimes used (like the word affine – see Affine connection) to refer to connections defined on the tangent bundle...