| 31. | Gaussian curvature, whereas a vertex with a negative angular deficit represents a concentration of " negative"
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| 32. | The unit disk " U " with the Poincar?metric has negative Gaussian curvature " 1.
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| 33. | The Gaussian curvature at a point can be recovered from parallel transport around increasingly small loops at the point.
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| 34. | It is not possible to specify a Riemannian metric on the torus with everywhere positive or everywhere negative Gaussian curvature.
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| 35. | For elliptical points where the Gaussian curvature is positive the intersection will either be empty or form a closed curve.
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| 36. | The fundamental result here is Gauss's theorema egregium, to the effect that Gaussian curvature is an intrinsic invariant.
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| 37. | Paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature.
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| 38. | Whereas the Gaussian curvature of a hyperboloid of one sheet is negative, that of a two-sheet hyperboloid is positive.
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| 39. | This is a special case of the Gauss Bonnet theorem which relates the integral of the Gaussian curvature to the Euler characteristic.
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| 40. | Give with justification a compact surface in \ mathbb { R } ^ 3 without boundary whose Gaussian curvature must change sign.
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