For a structure A with a non-positive value of this quantity, the universal cover of A is diffeomorphic to R-n according to the Cartan–Hadamard conjecture. A formulation of classical mechanics is based on the principle of least constraint and Hertz's principle of least [this property]. The sum of a boundary integral and surface integral of this quantity is equal to 2 pi times the Euler characteristic in the Gauss–Bonnet theorem. According to the Theorema Egregium, the (*) "Gaussian" type of this quantity is intrinsic. The norm of the derivative of the tangent vector with respect to arc length gives this quantity for a generic arc. It equals one over the radius for a circle. For 10 points, give this quantity usually symbolized kappa, which quantifies the deviation of a surface from flatness.
For a structure A with a non-positive value of this quantity, the universal cover of A is diffeomorphic to R-n according to the Cartan–Hadamard conjecture. A formulation of classical mechanics is based on the principle of least constraint and Hertz's principle of least [this property]. The sum of a boundary integral and surface integral of this quantity is equal to 2 pi times the Euler characteristic in the Gauss–Bonnet theorem. According to the Theorema Egregium, the (*) "Gaussian" type of this quantity is intrinsic. The norm of the derivative of the tangent vector with respect to arc length gives this quantity for a generic arc. It equals one over the radius for a circle. For 10 points, give this quantity usually symbolized kappa, which quantifies the deviation of a surface from flatness.
For a structure A with a non-positive value of this quantity, the universal cover of A is diffeomorphic to R-n according to the Cartan–Hadamard conjecture.
curvature [prompt on kappa or k; also accept things like “curvature of an [object]”] &lt;JL, Math&gt;