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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

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  • $\begingroup$ Maybe you can be more specific about what you are trying to accomplish. $\endgroup$ Mar 17, 2023 at 17:53
  • $\begingroup$ First of all I would like to try to simulate how a graph is changing over a discreet period of time t, and as a second step to be able to predict its structure over t+Δt. There is not much of research on the topic, I am just trying to brainstorm:) $\endgroup$ Mar 17, 2023 at 18:14

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