It is shown that a strong system of vector fields on a fiber bundle in the sense of [Mo] is induced from a principal fiber bundle if and only if each vertical vector field of the system is complete.

Representing the data of a string compactified on a circle in the background of H-flux in terms of the geometric data of a principal loop group bundle, we show that T-duality in type II string theory can be understood as the interchange of the momentum and winding homomorphisms of the principal loop group bundle, thus giving rise to a new interpretation of T-duality.

It is shown that a strong system of vector elds on a ber bundle in the sense of Mo] is induced from a principal ber bundle if and only if each vertical vector eld of the system is complete.

A regular vacuum solution in 5D gravity on the principal bundle with the U (1) structural group is proposed as a 4D wormhole. This solution has two null hypersurfaces where an interchange of the sign of some 5D metric components happens. For a 4D observer living on the base of this principal bundle this is a wormhole with two asymptotically flat Lorentzian (Euclidean) spacetimes connected by a ...

In [HL4] we study Yang-Mills functional on the space of connections on a principal GR-bundle over a closed, connected, nonorientable surface, where GR is any compact connected Lie group. In this sequel, we generalize the discussion in [AB] and [HL4]. We obtain explicit descriptions (as representation varieties) of Morse strata of Yang-Mills functional on orientable and nonorientable surfaces fo...

The aim of this article is to proof a necessary and sufficient condition for the existence of a Cartan connection on a principal bundle, cf. Theorem 3.2. After collecting the essentially well known facts1 to fix the terminology, abstract soldering forms and geometrizable principle bundles are defined to finally prove the existence criterion. 1 Principal bundles and associated bundles. Throughou...

We give a new construction of the holonomy groupoid regular foliation in terms partial connection on diffeological principal bundle germs transverse parametrisations, which may be viewed as systematisation Winkelnkemper’s original using ideas from gauge theory. extend these to construct novel for any foliated bundle, we prove sits at top hierarchy jet groupoids associated with bundle. This show...

We continue the investigation of Hopf-Galois extensions with central invariants started in [30]. Our objective is not to imitate algebraic geometry using Hopf-Galois extension but to understand their geometric properties. Let H be a finite-dimensional Hopf algebra over a ground field k. Our main object of study is an H-Galois extension U ⊇ O such that O is a central subalgebra of U . Let us bri...