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