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Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the ...