I am a beginner in topology and I am trying to define a model for some computations. My questions are speculative:
I am wondering what is the proper way to add time in a manifold so as to describe a time-varying process. For example, in riemannian geometry I can use a space with non-zero constant curvature(or even products of spaces with resulting non-constant curvature) and add a velocity vector in the tangent space, which describes time-varying properties of some entity. Is there any better way to represent temporal evolution within the riemannian framework?
In non-riemannian geometry I can use the corresponding manifolds of constant non-zero curvature(de-Sitter,anti-de-Sitter, or Minkowski). But isn't the time inherent in that manifolds so as not to have to add the extra vector as above?
Any thoughts would be really appreciated!
Best,
Kostas