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- Q3198879 subject Q7036087.
- Q3198879 subject Q7210663.
- Q3198879 subject Q7214705.
- Q3198879 subject Q8482188.
- Q3198879 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 tensor, 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 tensor. 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.".
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- Q3198879 wikiPageWikiLink Q7036087.
- Q3198879 wikiPageWikiLink Q7210663.
- Q3198879 wikiPageWikiLink Q7214705.
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- Q3198879 wikiPageWikiLink Q8482188.
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- Q3198879 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 tensor, and can be related to the curvature tensor.".
- Q3198879 label "Line element".