Does the inside of a sphere have negative curvature?
I mean does the inside surface of a hollow sphere have negative curvature?
the sphere is infinitely thin so it really has no inside or outside. The curvature is the same no matter how you look at it.
The answer is no.
A sphere (inside or outside) has positive curvature. Any direction in which you choose to measure, it will curve in the same direction. If the surface is extended far enough it will be closed.
An example of a shape that has a negative curvature is a saddle. If you go front-to-back it curves one way; but side-to-side it curves in a different direction. A saddle shape, if extended indefinitely, is open.
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