Differentiable Family of Contact Structures on a Non-Compact (2n-1)-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...

On images of continuous functions from a compact manifold to Euclidean space

Application of Hopf's lemma on contact CR-warped product submanifolds of a nearly Kenmotsu manifold

In this paper we consider contact CR-warped product submanifolds of the type $M = N_Ttimes_f N_perp$, of a nearly Kenmotsu generalized Sasakian space form $bar M(f_1‎, ‎f_2‎, ‎f_3)$ and by use of Hopf's Lemma we show that $M$ is simply contact CR-product under certain condition‎. ‎Finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case is dis...

DIFFERENTIABLE STRUCTURES 1. Classification of Manifolds

(1) Classify all spaces ludicrously impossible. (2) Classify manifolds only provably impossible (because any finitely presented group is the fundamental group of a 4-manifold, and finitely presented groups are not able to be classified). (3) Classify manifolds with a given homotopy type (sort of worked out in 1960’s by Wall and Browder if π1 = 0. There is something called the Browder-Novikov-Su...

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...