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Surface of constant positive / negative curvature example

Is the only body with positive constant curvature a sphere?
And constant negative curvature a hyperboloid?

Cheers in advance.
Original post by xfootiecrazeesarax
Is the only body with positive constant curvature a sphere?
And constant negative curvature a hyperboloid?

Cheers in advance.

Depends what you mean by "body". Any open subset of the sphere has positive constant curvature, of course. Liebmann's theorem states that the only regular C^2 closed surfaces in R^3 are spheres.

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