Characterization of Riemannian Manifolds with Weak Homology Group G2 (Following A. Gray).
Charles Ehresmann's concepts in differential geometry
We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.
Chern classes of vector bundles with singular connections
Si fa vedere che alcune classi di Chern di fibrati vettoriali complessi possono essere costruite non solo partendo da connessioni ma, sotto certe condizioni, anche da connessioni lineari singolari. Nel caso particolare del fibrato tangente possono essere costruite anche a partire da metriche singolari. Viene fatto uso in modo essenziale della -coomologia di de Rham (introdotta da Cheeger e Teleman).
Christoffer Symbols and Connection Forms on Infinite-Dimensional Fibre Bundles
Classes caractéristiques exotiques et -connexité des espaces de connexions
Le but de ce travail est double : d’une part, généraliser la construction des classes exotiques pour l’appliquer à d’autres problèmes géométriques que ceux issus des -structures ; d’autre part, préciser, grâce à la notion de -connexité, remplaçant avantageusement les formules de dérivation utilisées précédemment, l’argument d’invariance homotopique permettant d’obtenir des théorèmes de rigidité, montrant simultanément pourquoi la seule connexité des ensembles de connexions considérés ne suffit...
Classical differential geometry with Christoffel symbols of Ehresmann -connections
We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann -connection.
Classification of irreducible holonomies of torsion-free affine connections.
Classification of principal connections naturally induced on
We consider a vector bundle and the principal bundle of frames of . Let be a principal connection on and let be a linear connection on . We classify all principal connections on naturally given by and .
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.
Combinatorics of curvature, and the Bianchi identity.
Combinatorics of non-holonomous jets
Complex conformal connection on the locally conformal Kähler manifolds
Complex IP pseudo-Riemannian algebraic curvature tensors
Concerning Connections on Associated Bundles
Connection metrics of nonnegative curvature on vector bundles.
Connection theory on differentiable fibre bundles: A concise introduction.
Connections and 1-jet fiber bundles
Connections and regularity on the tangent and cotangent bundle.
Connections in 2-fibered manifolds
Connections in associated fibre bundles