| 1. | The sphere is the only surface with non-zero curvature where every point is umbilic.
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| 2. | The directrix'circle'becomes a curve with zero curvature, indistinguishable from a straight line.
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| 3. | Just as for zero curvature above-- talk 21 : 13, 21 October 2009 ( UTC)
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| 4. | Paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature.
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| 5. | On a surface of zero curvature, such as the Euclidean plane, the angles will sum to precisely ? radians.
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| 6. | Euclidean ) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature.
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| 7. | In addition, the Euclidean geometry ( which has zero curvature everywhere ) is not the only geometry that the plane may have.
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| 8. | As the radius increases the curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a hyperplane.
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| 9. | Since the space of meromorphic 1-forms is a 1-dimensional vector space over the curvature, zero curvature, or negative curvature.
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| 10. | Cartan geometries & mdash; those with zero curvature & mdash; are locally equivalent to homogeneous spaces, hence geometries in the sense of Klein.
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