Metallic conjugate connections

On Contravariant Product Conjugate Connections

Invariance properties for the covariant and contravariant connections on a Riemannian manifold with respect to an almost product structure are stated. Restricting to a distribution of the contravariant connections is also discussed. The particular case of the conjugate connection is investigated and properties of the extended structural and virtual tensors for the contravariant connections are ...

CONJUGATE SU(r)-CONNECTIONS AND HOLONOMY GROUPS

In this article we show that when the structure group of the reducible principal bundle P is SU(r) and Q ⊂ P is an SO(r)-subbundle of P , the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to [ r 2 ] , and use the estimate to show that for all odd prime r, if the holonomy group of the irreducible connection as above is simp...

Conjugate connections and differential equations on infinite dimensional manifolds

On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T M bijectively correspond to linear connections. In this paper we classify such structures for those Fréchet manifolds which can be considered as projective limits of Banach manifolds. We investigate also the relation between ordinary differential equations on Fréchet spaces and the linear connections on t...

Regular Connections among Generalized Connections

The properties of the space A of regular connections as a subset of the space A of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is determined whether A is dense in A or not. Moreover, it is proven that A has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoot...

Shen's Processes on Finslerian Connections