Circle of a sphere the Equator the only great circle. By contrast, all meridians of longitude, paired with their opposite meridian in the other hemisphere, form great circles. The diameter of the sphere which passes through the center of the circle is called its axis and the endpoints of this diameter are called its poles. A circle of a sphere can also be defined as the set of points at a given angular distance from a given pole. When the intersection of a sphere and a plane is not empty or a single point, it is a circle. This can be seen as follows:
Riemann sphere that group is called SO(3). In this sense, this is by far the most symmetric metric on the sphere. (The group of all isometries, known as O(3), is also 3-dimensional, but unlike SO(3) is not a connected space.) Conversely, let "S" denote the sphere (as an abstract smooth or topological manifold). By the uniformization theorem there exists a unique complex structure on "S", up to conformal equivalence. It follows that any metric on "S" is conformally equivalent to the round metric. All such metrics determine the same conformal geometry. The round metric is therefore not intrinsic to the Riemann sphere,