1. If a compact Lie group P acts on a completely regular topological space E then E is said to be a principal P-bundle if whenever the relation px — x holds for pÇzP, x£E it follows that p = e, the identity of P. The orbit space X = E/P is called the base space and the map tt: E—>X carrying y into its orbit P-y is called the projection. Suppose now that G is a Lie group, 77i a closed subgroup o...

A principal toric bundleM is a complex manifold equipped with a free holomorphic action of a compact complex torus T . Such a manifold is fibered over M/T , with fiber T . We discuss the notion of positivity in fiber bundles and define positive toric bundles. Given an irreducible complex subvariety X ⊂ M of a positive principal toric bundle, we show that either X is T -invariant, or it lies in ...

Any singularity free vector field X defined on an open set in a three-dimensional Euclidean space with curl X = 0 admits a complex line bundle Fa with a fibre-wise defined symplectic structure, a principal bundle Pa and a Heisenberg group bundle Ga . For the non-vanishing constant vector field X the geometry of Pa defines for each frequency a Schrödinger representation of any fibre of the Heise...

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

Let π : P → Mn be a principal G-bundle, and let L : JP → Λn(M) be a G-invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian l defined on C(P ), the bundle of connections on P .

With the standard fibre being a coset manifold, the transformation of a connection form in a fibre bundle under the action of the isometry group includes a dependence on the fibre coordinate. Elimination of the fibre coordinate from the transformation rule implies that the standard fibre is a Lie group and that the bundle is a principal bundle. The dependence on the fibre coordinate is consider...

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector...

Camera calibration has always been an essential component of photogrammetric measurement. Nowadays, with self-calibration being an integral and routinely applied operation within photogrammetric triangulation, especially in high-accuracy close-range measurement. Photogrammetric camera calibration is usually carried out together with the calculation of object coordinates such as principal distan...

Let G be a (real or complex) semisimple Lie group, whose Lie algebra g is endowed with a so called jkj{grading, i.e. a grading of the form g = g ?k g k , such that no simple factor of G is of type A 1. Let P be the subgroup corresponding to the subalgebra p = g 0 g k. The aim of this paper is to clarify the geometrical meaning of Cartan connections corresponding to the pair (G; P) and to study ...

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spe...