**Parallel Transport**

In general, parallel transport along a curve with respect to a connection defines isomorphisms between the tangent spaces at the points of the curve. If the connection is a Levi-Civita connection, then these isomorphisms are orthogonal – that is, they preserve the inner products on the various tangent spaces.

Read more about this topic: Levi-Civita Connection

### Other articles related to "parallel transport, parallel":

... The introduction of

**parallel transport**, covariant derivatives and connection forms gave a more conceptual and uniform way of understanding curvature, which ... by Levi-Civita (1917) who introduced the notion of

**parallel transport**on surfaces ... The monodromy of this equation defines

**parallel transport**for the connection, a notion introduced in this context by Levi-Civita ...

**Parallel Transport**

... See also

**parallel transport**Given a curve in the Euclidean plane and a vector at the starting point, the vector can be transported along the curve by requiring the moving vector to ...

**Parallel transport**can always be defined along curves on a surface using only the metric on the surface ...

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

**Parallel Transport**- Approximation: Schild's Ladder

...

**Parallel transport**can be discretely approximated by Schild's ladder, which takes finite steps along a curve, and approximates Levi-Civita parallelogramoids by ...

... instead, it is and restricted by the requirement that the

**parallel transport**between points and must be a linear combination of the base vectors in ... Here, expresses the

**parallel transport**of as linear combination of the base vectors in, i.e ... For such a metric, one can construct a dual connection to make , for

**parallel transport**using and ...

**Parallel Transport**-

**Parallel Transport**

...

**Parallel transport**of tangent vectors along a curve in the surface was the next major advance in the subject, due to Levi-Civita ...

**Parallel transport**along geodesics, the "straight lines" of the surface, can also easily be described directly ... field v(t) along a unit speed curve c(t), with geodesic curvature kg(t), is said to be

**parallel**along the curve if it has constant length the angle θ(t) that it makes with the velocity ...

### Famous quotes containing the words transport and/or parallel:

“One may disavow and disclaim vices that surprise us, and whereto our passions *transport* us; but those which by long habits are rooted in a strong and ... powerful will are not subject to contradiction. Repentance is but a denying of our will, and an opposition of our fantasies.”

—Michel de Montaigne (1533–1592)

“There isn’t a *Parallel* of Latitude but thinks it would have been the Equator if it had had its rights.”

—Mark Twain [Samuel Langhorne Clemens] (1835–1910)