For a complete Riemannian manifold, if Ricci's form of this quantity is bounded below by n minus one times k times the metric for some integer k, the manifold has diameter at most pi over square root of k, according to Myers' theorem.
For a complete Riemannian manifold, if Ricci's form of this quantity is bounded below by n minus one times k times the metric for some integer k, the manifold has diameter at most pi over square root of k, according to Myers' theorem. Any object for which the ";total"; form of this quantity is less than or equal to four pi must be an unknot, according to the Fabry- Milnor theorem. Two types of this quantity must sum to zero at every point on a minimal surface. The ";theorema egregium"; shows that another form of this quantity is invariant under local isometry, and shows it can be computed as the ratio of the determinants of the second andfirst fundamental forms. The integral of that type of this quantity over a surface is equal to two pi times the Euler characteristic of the surface. That ";Gaussian"; form of this property is the product of the two principal forms of this quantity. For 10 points, name this quantity that measures how much a manifold deviates from flatness.
For a complete Riemannian manifold, if Ricci's form of this quantity is bounded below by n minus one times k times the metric for some integer k, the manifold has diameter at most pi over square root of k, according to Myers' theorem.
curvature [accept Ricci  curvature, total  curvature, principal curvature, Gaussian curvature and other types of curvature]