Hermitian-Einstein Connections and Stable Vector Bundles Over Compact Complex Surfaces.
Higher covariant derivatives.
Higher order absolute differentiation with respect to generalized connections
Higher order Cartan connections.
Higher order Cartan connections
A Cartan connection associated with a pair is defined in the usual manner except that only the injectivity of is required. For an -th order connection associated with a bundle morphism the concept of Cartan order is defined, which for , and coincides with the classical definition. Results are obtained concerning the Cartan order of -th order connections that are the product of first order (Cartan) connections.
Higher order torsions of manifolds with connection
Higher order valued reduction theorems for classical connections
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
Higher-order differential equations represented by connections on prolongations of a fibered manifold.
The main goal of the present work is a generalization of the ideas, constructions and results from the first and second-order situation, studied in [63], [64] to that of an arbitrary finite-order one. Moreover, the investigation extends the ideas of [65] from the one-dimensional base X corresponding to O.D.E.
Holonomy Groups of a Fully Parallelizable Manifold
Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds
For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections...
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
Homotopien von Untermannigfaltigkeiten mit nicht ausgearteter zweiter Fundamentalform
Horizontal maps with homogeneity condition
Horizontal structures on fibre manifolds
How Charles Ehresmann's vision of geometry developed with time
In the mid fifties, Charles Ehresmann defined Geometry as "the theory of more or less rich structures, in which algebraic and topological structures are generally intertwined". In 1973 he defined it as the theory of differentiable categories, their actions and their prolongations. Here we explain how he progressively formed this conception, from homogeneous spaces to locally homogeneous spaces, to fibre bundles and foliations, to a general notion of local structures, and to a new foundation of differential...
Hyperholomorphic connections on coherent sheaves and stability
Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...