manicurv vs. manifold

[AntonioLao]

Differential geometry studies topology using calculus. The differential forms of the 1st derivatives are the 1D manifolds of the theory of curve. The 2nd derivatives form the 2D manifold or Riemann manifold. For this discussion, the 1D manifold is called manicurv.

The ratios of 1-space manicurv over the time manicurv formed the tangent velocity bundles. The ratios of velocity bundle over the time manicurv formed the acceleration bundles. The acceleration bundles can also be defined as the ratios of 1-space manicurv over the 2D time manifold. These two equivalent relations allow two distinct definitions for the vector field of acceleration. The point of contact between these relations gives a Lorentz invariance for all inner products of absolute acceleration and the fundamental metric such that

[math] \mathbf{a} \cdot \mathbf{r} =c^2[/math], where a is the absolute acceleration, r is the fundamental metric and c is the speed of light in vacuum.

[Guille]

What if I tell you that I have a proof both mathematical and logical that all manifolds are actually manicurves? What are the impplications of my demostration?

[AntonioLao]

then we dont need manifolds. And I need it to describe the quantization of spacetime.

[Guille]

then we dont need manifolds. And I need it to describe the quantization of spacetime.

Humm, thanks for the short info.

I wil work on the demostration.