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- List_of_coordinate_charts abstract "This article attempts to conveniently list articles on some of the most useful coordinate charts in some of the most useful examples of Riemannian manifolds.The notion of a coordinate chart is fundamental to various notions of a manifold which are used in mathematics.In order of increasing level of structure:topological manifoldsmooth manifoldRiemannian manifold and semi-Riemannian manifoldFor our purposes, the key feature of the last two examples is that we have defined a metric tensor which we can use to integrate along a curve, such as a geodesic curve. The key difference between Riemannian metrics and semi-Riemannian metrics is that the former arise from bundling positive-definite quadratic forms, whereas the latter arise from bundling indefinite quadratic forms.A four-dimensional semi-Riemannian manifold is often called a Lorentzian manifold, because these provide the mathematical setting for metric theories of gravitation such as general relativity.For many topics in applied mathematics, mathematical physics, and engineering, it is important to be able to write the most important partial differential equations of mathematical physicsheat equationLaplace equationwave equation(as well as variants of this basic triad) in various coordinate systems which are adapted to any symmetries which may be present. While this may be how many students first encounter a non-Cartesian coordinate chart, such as the cylindrical chart on E3 (three-dimensional Euclidean space), it turns out that these charts are useful for many other purposes, such as writing down interesting vector fields, congruences of curves, or frame fields in a convenient way.Listing commonly encountered coordinate charts unavoidably involves some real and apparent overlap, for at least two reasons:many charts exist in all (sufficiently large) dimensions, but perhaps only for certain families of manifolds such as spheres,many charts most commonly encountered for specific manifolds, such as spheres, actually can be used (with an appropriate metric tensor) for more general manifolds, such as spherically symmetric manifolds.Therefore, seemingly any attempt to organize them into a list involves multiple overlaps, which we have accepted in this list in order to be able to offer a convenient if messy reference.We emphasize that this list is far from exhaustive.".
- List_of_coordinate_charts wikiPageID "3207731".
- List_of_coordinate_charts wikiPageLength "7310".
- List_of_coordinate_charts wikiPageOutDegree "79".
- List_of_coordinate_charts wikiPageRevisionID "704625587".
- List_of_coordinate_charts wikiPageWikiLink Applied_mathematics.
- List_of_coordinate_charts wikiPageWikiLink Asymptotic_chart.
- List_of_coordinate_charts wikiPageWikiLink Asymptotic_curve.
- List_of_coordinate_charts wikiPageWikiLink Axial_projection_chart.
- List_of_coordinate_charts wikiPageWikiLink Axisymmetric_spacetime.
- List_of_coordinate_charts wikiPageWikiLink Bianchi_classification.
- List_of_coordinate_charts wikiPageWikiLink Cartesian_coordinate_system.
- List_of_coordinate_charts wikiPageWikiLink Cassini_bipolar_chart.
- List_of_coordinate_charts wikiPageWikiLink Cassini_toroidal_chart.
- List_of_coordinate_charts wikiPageWikiLink Category:Mathematics-related_lists.
- List_of_coordinate_charts wikiPageWikiLink Central_projection_chart.
- List_of_coordinate_charts wikiPageWikiLink Cylindrical_chart.
- List_of_coordinate_charts wikiPageWikiLink De_Sitter_model.
- List_of_coordinate_charts wikiPageWikiLink Definite_quadratic_form.
- List_of_coordinate_charts wikiPageWikiLink Differentiable_manifold.
- List_of_coordinate_charts wikiPageWikiLink Engineering.
- List_of_coordinate_charts wikiPageWikiLink Fiber_bundle.
- List_of_coordinate_charts wikiPageWikiLink General_relativity.
- List_of_coordinate_charts wikiPageWikiLink Geodesic.
- List_of_coordinate_charts wikiPageWikiLink Heat_equation.
- List_of_coordinate_charts wikiPageWikiLink Hopf_chart.
- List_of_coordinate_charts wikiPageWikiLink Hyperbolic_chart.
- List_of_coordinate_charts wikiPageWikiLink Isometry_(Riemannian_geometry).
- List_of_coordinate_charts wikiPageWikiLink Isothermal_chart.
- List_of_coordinate_charts wikiPageWikiLink Laplaces_equation.
- List_of_coordinate_charts wikiPageWikiLink Lie_group.
- List_of_coordinate_charts wikiPageWikiLink List_of_Fourier_analysis_topics.
- List_of_coordinate_charts wikiPageWikiLink List_of_differential_geometry_topics.
- List_of_coordinate_charts wikiPageWikiLink List_of_multivariable_calculus_topics.
- List_of_coordinate_charts wikiPageWikiLink Lists_of_mathematics_topics.
- List_of_coordinate_charts wikiPageWikiLink Manifold.
- List_of_coordinate_charts wikiPageWikiLink Mathematical_physics.
- List_of_coordinate_charts wikiPageWikiLink Maxwell_chart.
- List_of_coordinate_charts wikiPageWikiLink Mercator_projection.
- List_of_coordinate_charts wikiPageWikiLink Metric_tensor.
- List_of_coordinate_charts wikiPageWikiLink Metric_tensor_(general_relativity).
- List_of_coordinate_charts wikiPageWikiLink Minimal_surface.
- List_of_coordinate_charts wikiPageWikiLink Monge_chart.
- List_of_coordinate_charts wikiPageWikiLink Oblate_spheroidal_chart.
- List_of_coordinate_charts wikiPageWikiLink Parabolic_chart.
- List_of_coordinate_charts wikiPageWikiLink Partial_differential_equation.
- List_of_coordinate_charts wikiPageWikiLink Polar_spherical_chart.
- List_of_coordinate_charts wikiPageWikiLink Prolate_spheroidal_chart.
- List_of_coordinate_charts wikiPageWikiLink Pseudo-Riemannian_manifold.
- List_of_coordinate_charts wikiPageWikiLink Quadratic_form.
- List_of_coordinate_charts wikiPageWikiLink Radar_chart.
- List_of_coordinate_charts wikiPageWikiLink Riemannian_manifold.
- List_of_coordinate_charts wikiPageWikiLink Stereographic_projection.
- List_of_coordinate_charts wikiPageWikiLink Topological_manifold.
- List_of_coordinate_charts wikiPageWikiLink Toroidal_chart.
- List_of_coordinate_charts wikiPageWikiLink Upper_half_space_chart.
- List_of_coordinate_charts wikiPageWikiLink Wave_equation.
- List_of_coordinate_charts wikiPageWikiLink Weyl_vacuum.
- List_of_coordinate_charts wikiPageWikiLinkText "List of coordinate charts".
- List_of_coordinate_charts date "June 2010".
- List_of_coordinate_charts reason "Lead section unreferenced and unencyclopedic in tone, most list entries are red.".
- List_of_coordinate_charts wikiPageUsesTemplate Template:Cleanup.
- List_of_coordinate_charts subject Category:Mathematics-related_lists.
- List_of_coordinate_charts type List.
- List_of_coordinate_charts type List.
- List_of_coordinate_charts type Page.
- List_of_coordinate_charts comment "This article attempts to conveniently list articles on some of the most useful coordinate charts in some of the most useful examples of Riemannian manifolds.The notion of a coordinate chart is fundamental to various notions of a manifold which are used in mathematics.In order of increasing level of structure:topological manifoldsmooth manifoldRiemannian manifold and semi-Riemannian manifoldFor our purposes, the key feature of the last two examples is that we have defined a metric tensor which we can use to integrate along a curve, such as a geodesic curve. ".
- List_of_coordinate_charts label "List of coordinate charts".
- List_of_coordinate_charts sameAs Q6613669.
- List_of_coordinate_charts sameAs Q6613669.
- List_of_coordinate_charts wasDerivedFrom List_of_coordinate_charts?oldid=704625587.
- List_of_coordinate_charts isPrimaryTopicOf List_of_coordinate_charts.