In geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the manifold...

Christoffel's symbols to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the...

connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over...

measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. For flat connections, the...

_{x_{t}}:T_{x_{0}}M\to T_{x_{t}}M} the parallel transport map along x t {\displaystyle x_{t}} . The parallel transport maps are related to the covariant derivative...

a notion of parallel transport, which is a method for transporting tangent vectors along curves. This also defines a parallel transport on the frame...

norm of kg, it follows that parallel transport for an arbitrary curve can be obtained as the limit of the parallel transport on approximating piecewise...

can define the parallel transport of a vector v at a point P along a curve γ starting at P. For each point x of γ, the parallel transport of v at x will...

Euclidean space with imaginary radius and imaginary timelike coordinate. Parallel transport of polarization vectors along such sphere gives rise to Thomas precession...

of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and...

generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only affinely parametrized geodesics...

The environmental effects of transport are significant because transport is a major user of energy, and burns most of the world's petroleum. This creates...

without reference to a metric, and many additional concepts follow: parallel transport, covariant derivatives, geodesics, etc. also do not require the concept...

turning of this path. Thus the orientation of the pendulum undergoes parallel transport. For the original Foucault pendulum, the path is a circle of latitude...

transport the vector (keeping it parallel) first along the equator to the point P, then drag it along a meridian to the N pole, and finally transport...

Furthermore, many of the features of the covariant derivative still remain: parallel transport, curvature, and holonomy. The missing ingredient of the connection...

effect of parallel transporting a vector between two points along two curves. The discrepancy between the results of these two parallel transport routes...

Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form. These concepts were put...

numerical approaches to neutron transport have become prevalent. Today, with massively parallel computers, neutron transport is still under very active development...

about the vertical axis. 2D computer graphics#Translation Advection Parallel transport Rotation matrix Scaling (geometry) Transformation matrix Translational...

Parallel translation may refer to: parallel transport, in mathematics parallel text, in translation This disambiguation page lists articles associated...

that the space of velocities in relativity is hyperbolic, and so parallel transport of a vector (the gyroscope's angular velocity) around a circle (its...

remaining unaffected. Parallel Transport Unfolding : Replaces the Dijkstra path-based geodesic distance estimates with parallel transport based approximations...

Rail transport (also known as train transport) is a means of transport using wheeled vehicles running in tracks, which usually consist of two parallel steel...

Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided...

theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge information...

obey conservation principles and those that do not. In the case of parallel transport on a sphere, the distinction is clear: a Riemannian manifold has a...

Transport (in British English) or transportation (in American English) is the intentional movement of humans, animals, and goods from one location to...

differential operators on certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method...

regards to properties of parallel transport of vectors and their length. By demanding that a manifold have an affine parallel transport in such a way that the...