There the idea of parallel transport was found to be helpful.

This always has a unique solution, called the parallel transport of v along c.

This also defines a parallel transport on the frame bundle.

Or, vice versa, parallel transport is the local realization of a connection.

In differential geometry, an analogous role is played by parallel transport.

The Foucault pendulum is a physical example of parallel transport.

Parallel transport can be extended immediately to piecewise C curves.

This isomorphism is known as the parallel transport map associated to the curve.

Parallel transport along geodesics, the "straight lines" of the surface, can also easily be described directly.

Parallel transport along geodesics, the "straight lines" of the surface, is easy to define.

The covariant derivative can in turn be recovered from parallel transport.

The local theory concerns itself primarily with notions of parallel transport and holonomy.

Such tangent vectors are said to be parallel transports of each other.

Parallel transport of these complex structures gives the required quaternionic structure on M.

The idea of sliding the one straight line along the other gives way to the more general notion of parallel transport.

This procedure defines parallel transport of a local vector in space-time.

Mathematically the device performs parallel transport along the path it travels.

Further generalizations of parallel transport are also possible.

However, he can start by moving off in the direction of the local vector itself, and in this case parallel transport is well defined.

Monodromy, or representations of the fundamental group by parallel transport on flat bundles.

Such curve lifting may sometimes be thought of as the parallel transport of reference frames.

An equivalent view of this effect is that the result of parallel transport in a curved space depends on the path taken.

This is a discrete approximation of the continuous process of parallel transport.

There is only one obvious notion of parallel transport and only one natural connection.

This identification of the tangent planes along the curve corresponds to parallel transport.