The main objective for this thesis is the construction of a tensor bundle on a diffeological space X. Thereby getting access to the exterior bundle of antisymmetric tensors on X, and smooth sections here on i.e. differential forms. We shall list certain requirements that any reasonable tensor bundle on a diffeological space should fulfil. And show that the given construction fulfil these requir...

Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.

We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold, under which spacetime addmits Dirac eigenvalues as observables, are derived. Typeset using REVTEX

We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold, under which spacetime addmits Dirac eigenvalues as observables, are derived. Typeset using REVTEX

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = TM ⊗ νM is equipped with an almost metric connection ∇̃ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂ − ∇̃ with the usual derivative ∂ in Rm is almost ∇̃-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two subbundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either b...

The bundle of Dirac spinors is used for describing particles with half-integer spin in general relativity and in quantum field theory. It is a special four-dimensional complex vector-bundle over the space-time manifold M . Let’s remind that the space-time manifold M itself is a four-dimensional real manifold equipped with a Minkowski type metric g of the signature (+,−,−,−). Apart from g, the s...

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...

We deal with the construction of covariant derivatives for some quite general Ehresmann connections on fibre bundles. show how introduction a vertical endomorphism allows separately both and horizontal distributions connection which can then be glued together total space. give applications across an important class tangent bundle cases, frame bundles Hopf bundle.