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I am looking for (at least) one example of the following manifolds:

  1. Flat, homogeneous and isotropic
  2. Curved, homogeneous and isotropic
  3. Flat, non-homogeneous and isotropic
  4. Flat, homogeneous and non-isotropic
  5. Curved, non-homogeneous and isotropic
  6. Curved, homogeneous and non-isotropic
  7. Flat, non-homogeneous and non-isotropic
  8. Curved, non-homogeneous and non-isotropic

By isotropic, I mean isotropic at least about some specific point.

This is what comes to (my) mind:

  1. Euclidean space
  2. (2-)Sphere
  3. Euclidean space with one point removed / Vector space
  4. Minkowski space
  5. Sphere with one point removed?
  6. ?
  7. Euclidean space with two point removed?
  8. A generic manifold

I hope you can provide some better examples.

0 Answers0