On weakly symmetric manifolds with a type of semi-symmetric non-metric connection
The object of the present paper is to study weakly symmetric manifolds admitting a type of semi-symmetric non-metric connection.
On Weakly -Symmetric Manifolds
The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...
Projectively invariant distances for affine and projective structures
Propriétés projectives des espaces symétriques affines
On donne une description algébrique de l’ensemble des classes d’isomorphisme d’espaces symétriques affines connexes, simplement connexes et projectivement plats. On en déduit une classification des espaces symétriques affines connexes et projectivement plats et on détermine tous les espaces symétriques affines connexes admettant une transformation projective non affine.
Recent advances in the theory of holonomy
Reductive homogeneous spaces and nonassociative algebras
The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.
Relations between Finsler and affine connections
Relèvement horizontal des connexions linéaires au fibré vectoriel associé avec le fibré principal des repères linéaires
Relèvements horizontaux de tenseurs de type (1,1) au fibré E = TM⊗T* M
Remarkable vector fields in deformation algebras: Retrospective and perspective. (Champs des vecteurs remarquables dans l'algèbre de déformation: Rétrospective et perspective.)
Remarks on F-planar curves and their generalizations
Generalized planar curves (A-curves) are more general analogues of F-planar curves and geodesics. In particular, several well known geometries are described by more than one affinor. The best known example is the almost quaternionic geometry. A new approach to this topic (A-structures) was started in our earlier papers. In this paper we expand the concept of A-structures to projective A-structures.
Ricci and Bianchi identities for -normal -linear connections on .
Ricci identities in the space of non-symmetric affine connexion
Ricci type identities for basic differentiation and curvature tensors in Otsuki spaces.
Ricci type identities for non-basic differentiation in Otsuki spaces.
Ricci Type Identities In A Subspace Of Space Of Non-Symmetric Affine Connexion
-metrische Zusammenhänge in isotropen Mannigfaltigkeiten. (- metric connections in isotropic manifolds).
Scalar differential concomitants of first order of a symmetric connexion in the two-dimensional space and their applications
Shells of monotone curves
We determine in the form of curves corresponding to strictly monotone functions as well as the components of affine connections for which any image of under a compact-free group of affinities containing the translation group is a geodesic with respect to . Special attention is paid to the case that contains many dilatations or that is a curve in . If is a curve in and is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...