Some characteristics of curvature tensors of nonsymmetric affine connexion.
Some maximal graduation classes and their Riemannian properties
Some vector subbundles of a cotangent bundle of order 2
Spaces with a covariant constant linear geometric object
Spaces with non-symmetric affine connection.
Special compositions in affinely connected spaces without a torsion
2000 Mathematics Subject Classification: 53B05, 53B99.Let AN be an affinely connected space without a torsion. With the help of N independent vector fields and their reciprocal covectors is built an affinor which defines a composition Xn ×Xm (n+m = N). The structure is integrable. New characteristics by the coefficients of the derivative equations are found for special compositions, studied in [1], [3]. Two-dimensional manifolds, named as bridges, which cut the both base manifolds of the composition...
Statistical manifolds with maximal automorphisms group.
Statistical structures on tangent bundles.
Submanifolds of an even-dimensional manifold structured by a -parallel connection.
Sur la notion de la dérivée covariante et de la dérivée de Lie
Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope
En utilisant la version de Spencer-Goldschmidt du théorème de Cartan-Kähler nous étudions les conditions nécessaires et suffisantes pour qu’un système d’équations différentielles ordinaires du second ordre soit le système d’Euler-Lagrange associé à un lagrangien régulier. Dans la thèse de Z. Muzsnay cette technique a été déjà appliquée pour donner une version moderne du papier classique de Douglas qui traite le cas de la dimension 2. Ici nous considérons le cas où la dimension est arbitraire, nous...
Tensor approach to multidimensional webs
An anholonomic -web of dimension is considered as an -tuple of -dimensional distributions in general position. We investigate a family of -tensor fields (projectors and nilpotents associated with a web in a natural way) which will be used for characterization of all linear connections on a manifold preserving the given web.
The double exponential map and covariant derivation.
The equations of structure of an -linear connection in the bundle of accelerations.
The osculating hyperquadrics of the three-component distribution in affine space
The Tanaka-Webster connection for almost -manifolds and Cartan geometry
We prove that a CR-integrable almost -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...
The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Élie Cartan...
Torsion and the second fundamental form for distributions
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.
Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Traceless cubic forms on statistical manifolds and Tchebychev geometry
Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.