If our universe has intrinsic curvature in a higher dimension, would that mean the 3 dimensions that we live in would be curved? and if so would the lower dimensions exhibit intrinsic or extrinsic curvature as a result of the curvature in the higher dimension.

A follow up question would be, could the lower dimensions have intrinsic curvature without exhibiting any extrinsic curvature in higher dimensions

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    $\begingroup$ what do you mean by the universe having intrinsic curvature "in a higher dimension"? $\endgroup$
    – ACuriousMind
    Aug 20 '21 at 11:40
  • $\begingroup$ Our 3D universe exhibits intrinsic curvature, if our universe was 4D and it had intrinsic curvature would we be able to notice it in our 3d world $\endgroup$ Aug 20 '21 at 11:47
  • 1
    $\begingroup$ Given that you tagged this with general relativity, our universe is 4D - three spatial and one temporal dimension. I'm not quite following you. $\endgroup$
    – ACuriousMind
    Aug 20 '21 at 11:48
  • $\begingroup$ 4 spatial i meant, I apologize if it’s the wrong tag feel free to move it or remove it $\endgroup$ Aug 20 '21 at 11:57
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    $\begingroup$ Do you mean like our actual Universe? Curved 4D spacetime, with very nearly flat space at large scales. $\endgroup$
    – D. Halsey
    Aug 20 '21 at 13:24

A cylinder is a simple example which shows that curvature in one dimension does not imply curvature in another. We could imagine a universe which is (locally) flat in the 4 space-time dimension, but is curved in one or more other dimensions. These other dimensions could have a large or small amount of curvature, and in a SF context might be seen as 'like' space-time in some respect. In a Physics context though the difficult question is what they are. Is there anything we can measure or perceive which could be interpreted as a 'dimension' orthogonal to space-time?

  • $\begingroup$ that curvature in one dimension does not imply curvature in another- is this always the case? $\endgroup$ Aug 20 '21 at 14:47
  • $\begingroup$ Curvature in one dimension does not on its own imply curvature in another dimension. There would need to be other conditions linking the dimensions together. $\endgroup$
    – Peter
    Aug 21 '21 at 4:37

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