4 papers · 1 filter
Generalized pseudo-Riemannian geometry
Michael Kunzinger, Roland Steinbauer
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving s…
Diffeomorphism invariant Colombeau Algebras. Part I: Local theory
Roland Steinbauer
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space…
Nonlinear distributional geometry and general relativity
Roland Steinbauer
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special…
Foundations of a nonlinear distributional geometry
Michael Kunzinger, Roland Steinbauer
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tens…