parallel transport
Curve-following vector movement
Parallel transport is a way of moving a vector along a curve while keeping it as constant as possible given the geometry of the space.
On a flat surface, this is straightforward—the vector maintains its direction.
On curved surfaces like a sphere, parallel transport reveals the curvature: a vector carried around a closed path may return pointing in a different direction than it started.
The concept is fundamental in differential geometry and general relativity, where it helps define how objects move through curved spacetime.
A joining or relation
- covariant derivativeGeneralized derivative on manifolds
- geodesicShortest curved-surface path
- torsionRotational strain force
- path dependencePast decisions constrain future options
Gravity as curved spacetime
- spacetimeMerged dimensional framework
- gravitational fieldRegion where masses attract
- free fallUnimpeded gravitational descent
- tetradGroup of four units
Intrinsic surface bending measure
connection
A joining or relation
- covariant derivativeGeneralized derivative on manifolds
- geodesicShortest curved-surface path
- torsionRotational strain force
general relativity
Gravity as curved spacetime
- spacetimeMerged dimensional framework
- gravitational fieldRegion where masses attract
- free fallUnimpeded gravitational descent
Gaussian curvature
Intrinsic surface bending measure
- Gauge TheoryYang-Mills theory, covariant derivative, connection
- Riemannian geometrygeodesics, Christoffel symbols
- spacetimespacetime, space-time, four-dimensional, tesseract, hypercube
- Spacetime Geometryspacetime, curvature, geodesics, general relativity, manifolds
- connectionslink, links, connect, connection, tie
- fiber bundlesfiber, section, sections, trivialization, connection
transport, parallel, transported, parallels, transports, unparalleled, transporting, transporter, parallelism