**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":

... 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 ...

... The introduction of

**parallel transport**, covariant derivatives and connection forms gave a more conceptual and uniform way of understanding curvature, which not only ... given a geometric interpretation 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**- 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 approximate parallelograms ...

**Parallel Transport**-

**Parallel Transport**

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**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 ...

**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 remain

**parallel**to the original one ...

**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 ...

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

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—Michel de Montaigne (1533–1592)

“The *parallel* between antifeminism and race prejudice is striking. The same underlying motives appear to be at work, namely fear, jealousy, feelings of insecurity, fear of economic competition, guilt feelings, and the like. Many of the leaders of the feminist movement in the nineteenth-century United States clearly understood the similarity of the motives at work in antifeminism and race discrimination and associated themselves with the anti slavery movement.”

—Ashley Montagu (b. 1905)