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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 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.".
- Line_element wikiPageID "855138".
- Line_element wikiPageLength "8287".
- Line_element wikiPageOutDegree "69".
- Line_element wikiPageRevisionID "692565512".
- Line_element wikiPageWikiLink Affine_space.
- Line_element wikiPageWikiLink Arc_length.
- Line_element wikiPageWikiLink Cartesian_coordinate_system.
- Line_element wikiPageWikiLink Category:Affine_geometry.
- Line_element wikiPageWikiLink Category:General_relativity.
- Line_element wikiPageWikiLink Category:Riemannian_geometry.
- Line_element wikiPageWikiLink Category:Special_relativity.
- Line_element wikiPageWikiLink Coordinate_system.
- Line_element wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Line_element wikiPageWikiLink Curvature.
- Line_element wikiPageWikiLink Curve.
- Line_element wikiPageWikiLink Curvilinear_coordinates.
- Line_element wikiPageWikiLink Cylindrical_coordinate_system.
- Line_element wikiPageWikiLink Differentiable_function.
- Line_element wikiPageWikiLink Differential_(infinitesimal).
- Line_element wikiPageWikiLink Dimension.
- Line_element wikiPageWikiLink Displacement_(vector).
- Line_element wikiPageWikiLink Event_(relativity).
- Line_element wikiPageWikiLink First_fundamental_form.
- Line_element wikiPageWikiLink Four-dimensional_space.
- Line_element wikiPageWikiLink Four-vector.
- Line_element wikiPageWikiLink Frenet–Serret_formulas.
- Line_element wikiPageWikiLink General_relativity.
- Line_element wikiPageWikiLink Geodesic.
- Line_element wikiPageWikiLink Geometry.
- Line_element wikiPageWikiLink Gravity.
- Line_element wikiPageWikiLink Infinitesimal.
- Line_element wikiPageWikiLink Inner_product_space.
- Line_element wikiPageWikiLink Integral.
- Line_element wikiPageWikiLink Inverse_function.
- Line_element wikiPageWikiLink Kronecker_delta.
- Line_element wikiPageWikiLink List_of_integration_and_measure_theory_topics.
- Line_element wikiPageWikiLink Lorentz_transformation.
- Line_element wikiPageWikiLink Manifold.
- Line_element wikiPageWikiLink Mass.
- Line_element wikiPageWikiLink Matrix_(mathematics).
- Line_element wikiPageWikiLink Metric_space.
- Line_element wikiPageWikiLink Metric_tensor.
- Line_element wikiPageWikiLink Minkowski_space.
- Line_element wikiPageWikiLink Orthogonal_coordinates.
- Line_element wikiPageWikiLink Parameter.
- Line_element wikiPageWikiLink Physics.
- Line_element wikiPageWikiLink Polar_coordinate_system.
- Line_element wikiPageWikiLink Position_(vector).
- Line_element wikiPageWikiLink Raising_and_lowering_indices.
- Line_element wikiPageWikiLink Ricci_calculus.
- Line_element wikiPageWikiLink Riemann_curvature_tensor.
- Line_element wikiPageWikiLink Space.
- Line_element wikiPageWikiLink Spacetime.
- Line_element wikiPageWikiLink Special_relativity.
- Line_element wikiPageWikiLink Spherical_coordinate_system.
- Line_element wikiPageWikiLink Surface.
- Line_element wikiPageWikiLink Three-dimensional_space_(mathematics).
- Line_element wikiPageWikiLink Time.
- Line_element wikiPageWikiLink Trajectory.
- Line_element wikiPageWikiLink Volume_element.
- Line_element wikiPageWikiLink File:Line_element.svg.
- Line_element wikiPageWikiLinkText "Line element".
- Line_element wikiPageWikiLinkText "line element".
- Line_element wikiPageUsesTemplate Template:About.
- Line_element wikiPageUsesTemplate Template:Ell.
- Line_element wikiPageUsesTemplate Template:For.
- Line_element wikiPageUsesTemplate Template:Main.
- Line_element wikiPageUsesTemplate Template:Reflist.
- 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 tensor, and can be related to the curvature tensor.".
- Line_element label "Line element".
- Line_element sameAs Q3198879.
- Line_element sameAs Viivaelementti.
- Line_element sameAs m.03hkxt.
- Line_element sameAs Linjeelement.
- Line_element sameAs Q3198879.
- Line_element wasDerivedFrom Line_element?oldid=692565512.
- Line_element isPrimaryTopicOf Line_element.