How can I prove that a one sheet hyperboloid has a negative curvature? Also, how can I show that this shape expands to infinity?
2026-04-01 09:38:17.1775036297
Curvature of a hyperboloid of one sheet
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Represent it (locally) as graph of a function, compute the Hessian, and show that its determinant is negative. The graph "expands to infinity" because for every pair $(x,y)$ outside the unit circle, you can find an appropriate $z$.