geodesics's Usage Examples:

In a Riemannian manifold or submanifold geodesics are characterised by the property of having vanishing geodesic curvature.

such instances, the proper times along several geodesics will not in general be the same.

For some geodesics in such instances, it is possible for a curve.

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks.

the time-like geodesics into the future, it is impossible for the boundary of the region they form to be generated by the null geodesics from the surface.

In spaces with curvature, straight lines are replaced by geodesics.

the geometry of geodesics.

Given a system of parametrized geodesics, one can specify a class of affine connections having those geodesics, but differing.

counting simple closed geodesics on hyperbolic Riemann surfaces by finding a relationship to volume calculations on moduli space.

wormhole, modified, however, by the fact that the metric and therefore the geodesics of equatorial cross sections of the wormhole are not straight lines, rather.

equidistant curves, parallel geodesics and geodesics sharing a common perpendicular, respectively.

While in Euclidean geometry two geodesics can either intersect.

These great circles are the geodesics of the sphere.

Length minimizing curves can always be positively reparametrized to be geodesics, and any geodesic must satisfy the Euler–Lagrange equation for E[γ].

Closed geodesics can be characterized by means of a variational principle.

light cone of a given observer is studied, it can be found that null geodesics moving orthogonally to ∂ y {\displaystyle \partial _{y}} spiral inwards.

a convex polyhedron is a net obtained by cutting the polyhedron along geodesics (shortest paths) through its faces.

The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner.

Such geodesics are called prime geodesics because, among other things, they obey an asymptotic distribution.

oricircle, or limit circle) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction.

It is frequently said that geodesics are "straight lines in curved space".

Non-spinning bodies move in geodesics, whereas spinning bodies move in slightly different orbits.

diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable.

Synonyms:

geodetic; geodesical;

Antonyms:

straight line; natural object; inactivity;