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- Line_element abstract "In geometry, the line element or length element can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parameterizing the given curve by Frenet–Serret formulas. As such, a line element is then naturally a function of the metric, and can be related to the curvature tensor. It is usually denoted by s or ℓ, and differentials of this are then written ds or dℓ.Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved manifold with a metric. For example, if a massive object causes some curvature in spacetime, the trajectory of an object with negligible mass over that curvature would follow the line element according to the geodesic equation.".
- Line_element wikiPageID "855138".
- Line_element wikiPageRevisionID "604222239".
- Line_element hasPhotoCollection Line_element.
- Line_element subject Category:Affine_geometry.
- Line_element subject Category:General_relativity.
- Line_element subject Category:Riemannian_geometry.
- Line_element subject Category:Special_relativity.
- Line_element comment "In geometry, the line element or length element can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parameterizing the given curve by Frenet–Serret formulas. As such, a line element is then naturally a function of the metric, and can be related to the curvature tensor.".
- Line_element label "Line element".
- Line_element sameAs m.03hkxt.
- Line_element sameAs Q3198879.
- Line_element sameAs Q3198879.
- Line_element wasDerivedFrom Line_element?oldid=604222239.
- Line_element isPrimaryTopicOf Line_element.