The Weyl bundle as a differentiable manifold

The Weyl bundle as a differentiable manifold

Construction of an infinite dimensional differentiable manifold R∞ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P ∗ p M [[~]], ◦) and a Weyl algebra bundle (P∗M[[~]], ◦) are presented. Continuity of the ◦-product in the Tichonov topology is proved. Construction of the ∗-product of the Fedosov type in terms of theory of connectio...

The Real Cohomology Ring of a Sphere Bundle over a Differentiable Manifold

Implications of Non-Differentiable Entropy on a Space-Time Manifold

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...

Data-based Manifold Reconstruction via Tangent Bundle Manifold Learning

The goal of Manifold Learning (ML) is to find a description of low-dimensional structure of an unknown q-dimensional manifold embedded in high-dimensional ambient Euclidean space R p , q < p, from their finite samples. There are a variety of formulations of the problem. The methods of Manifold Approximation (MA) reconstruct (estimate) the manifold but don’t find a low-dimensional parameterizati...

On the G 2 bundle of a Riemannian 4 - manifold

We expose the theory of the construction of a natural G 2 structure on the unit sphere tangent bundle SM of any given orientable Riemannian 4-manifold M , as laid in [4]. This time we work in the context of metric connections, or geometry with torsion. 1 Recalling the theory By a G 2 manifold it is understood a 7 dimensional Riemannian manifold with holonomy group contained in G 2 = Aut(O). The...