A geodesic circle is either "the
locus on a
surface at a constant
geodesic distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...
from a fixed
point" or a
curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...
of constant
geodesic curvature.
A geodesic disk is the region on a surface bounded by a geodesic circle.
In contrast with the ordinary
circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
and
disk, the geodesic circle is not necessarily a
plane curve and the geodesic disk is not necessarily a
planar surface.
They can be used to define ''
Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature of a smooth Surface (topology), surface in three-dimensional space at a point is the product of the principal curvatures, and , at the given point:
K = \kappa_1 \kappa_2.
For ...
''.
References
Geodesic (mathematics)
Circles
{{Riemannian-geometry-stub