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

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

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

function, whereas differentiation is used to define curvature and parallel transport. Any smooth surface in three-dimensional Euclidean space is a Riemannian...

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...

manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical...

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...

_{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...

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...

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...

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

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...

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

The health and environmental impact of transport is significant because transport burns most of the world's petroleum. This causes illness and deaths from...

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

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

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...

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...

heave. 2D computer graphics#Translation Advection Change of basis Parallel transport Rotation matrix Scaling (geometry) Transformation matrix Translational...

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

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...

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

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

sectional curvature. The construction of a parallel vector field along any path is automatic via parallel transport; the nontriviality in the case of a loop...

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

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...

geometries to be worked out in detail: it is based on a special type of parallel transport [...using] worldlines of light-signals in four-dimensional space-time...

well as curvature. In Cartan's geometry of bundles, the concept of parallel transport is more fundamental than that of distance, the centerpiece of Riemannian...