Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Differentiable_manifold> ?p ?o }
- Differentiable_manifold abstract "In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since each chart lies within a linear space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.In formal terms, a differentiable manifold is a topological manifold with a globally defined differential structure. Any topological manifold can be given a differential structure locally by using the homeomorphisms in its atlas and the standard differential structure on a linear space. To induce a global differential structure on the local coordinate systems induced by the homeomorphisms, their composition on chart intersections in the atlas must be differentiable functions on the corresponding linear space. In other words, where the domains of charts overlap, the coordinates defined by each chart are required to be differentiable with respect to the coordinates defined by every chart in the atlas. The maps that relate the coordinates defined by the various charts to one another are called transition maps.Differentiability means different things in different contexts including: continuously differentiable, k times differentiable, smooth, and holomorphic. Furthermore, the ability to induce such a differential structure on an abstract space allows one to extend the definition of differentiability to spaces without global coordinate systems. A differential structure allows one to define the globally differentiable tangent space, differentiable functions, and differentiable tensor and vector fields. Differentiable manifolds are very important in physics. Special kinds of differentiable manifolds form the basis for physical theories such as classical mechanics, general relativity, and Yang–Mills theory. It is possible to develop a calculus for differentiable manifolds. This leads to such mathematical machinery as the exterior calculus. The study of calculus on differentiable manifolds is known as differential geometry.".
- Differentiable_manifold thumbnail Nondifferentiable_atlas.png?width=300.
- Differentiable_manifold wikiPageExternalLink Manifolds_and_Differential_Geometry.html?id=QqHdHy9WsEoC.
- Differentiable_manifold wikiPageExternalLink SmoothManifold.html.
- Differentiable_manifold wikiPageExternalLink Geom.
- Differentiable_manifold wikiPageID "2119219".
- Differentiable_manifold wikiPageLength "55232".
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- Differentiable_manifold wikiPageRevisionID "682358315".
- Differentiable_manifold wikiPageWikiLink 2-form.
- Differentiable_manifold wikiPageWikiLink 3-manifold.
- Differentiable_manifold wikiPageWikiLink 4-manifold.
- Differentiable_manifold wikiPageWikiLink 5-manifold.
- Differentiable_manifold wikiPageWikiLink A_fortiori_argument.
- Differentiable_manifold wikiPageWikiLink Active_and_passive_transformation.
- Differentiable_manifold wikiPageWikiLink Active_transformation.
- Differentiable_manifold wikiPageWikiLink Affine_connection.
- Differentiable_manifold wikiPageWikiLink Affine_space.
- Differentiable_manifold wikiPageWikiLink Affine_transformation.
- Differentiable_manifold wikiPageWikiLink Albert_Einstein.
- Differentiable_manifold wikiPageWikiLink Algebra_(ring_theory).
- Differentiable_manifold wikiPageWikiLink Algebra_over_a_field.
- Differentiable_manifold wikiPageWikiLink Algebraic_geometry.
- Differentiable_manifold wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Differentiable_manifold wikiPageWikiLink Analytic_function.
- Differentiable_manifold wikiPageWikiLink Annals_of_Mathematics.
- Differentiable_manifold wikiPageWikiLink Antisymmetric_tensor.
- Differentiable_manifold wikiPageWikiLink Arc_length.
- Differentiable_manifold wikiPageWikiLink Atlas_(mathematics).
- Differentiable_manifold wikiPageWikiLink Atlas_(topology).
- Differentiable_manifold wikiPageWikiLink Banach_manifold.
- Differentiable_manifold wikiPageWikiLink Banach–Stone_theorem.
- Differentiable_manifold wikiPageWikiLink Bernhard_Riemann.
- Differentiable_manifold wikiPageWikiLink Biholomorphic.
- Differentiable_manifold wikiPageWikiLink Biholomorphism.
- Differentiable_manifold wikiPageWikiLink C*-algebra.
- Differentiable_manifold wikiPageWikiLink Calculus.
- Differentiable_manifold wikiPageWikiLink Carl_Friedrich_Gauss.
- Differentiable_manifold wikiPageWikiLink Category:Smooth_manifolds.
- Differentiable_manifold wikiPageWikiLink Category_theory.
- Differentiable_manifold wikiPageWikiLink Chain_rule.
- Differentiable_manifold wikiPageWikiLink Christoffel_symbols.
- Differentiable_manifold wikiPageWikiLink Circle.
- Differentiable_manifold wikiPageWikiLink Classical_mechanics.
- Differentiable_manifold wikiPageWikiLink Closed_and_exact_differential_forms.
- Differentiable_manifold wikiPageWikiLink Closed_form_(calculus).
- Differentiable_manifold wikiPageWikiLink Compact_space.
- Differentiable_manifold wikiPageWikiLink Completion_(algebra).
- Differentiable_manifold wikiPageWikiLink Completion_(ring_theory).
- Differentiable_manifold wikiPageWikiLink Complex_analytic_geometry.
- Differentiable_manifold wikiPageWikiLink Complex_field.
- Differentiable_manifold wikiPageWikiLink Complex_geometry.
- Differentiable_manifold wikiPageWikiLink Complex_number.
- Differentiable_manifold wikiPageWikiLink Connection_(mathematics).
- Differentiable_manifold wikiPageWikiLink Contact_(mathematics).
- Differentiable_manifold wikiPageWikiLink Continuously_differentiable.
- Differentiable_manifold wikiPageWikiLink Convenient_vector_space.
- Differentiable_manifold wikiPageWikiLink Coordinate_system.
- Differentiable_manifold wikiPageWikiLink Coordinate_transformation.
- Differentiable_manifold wikiPageWikiLink Cotangent_bundle.
- Differentiable_manifold wikiPageWikiLink Cotangent_space.
- Differentiable_manifold wikiPageWikiLink Covariance.
- Differentiable_manifold wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Differentiable_manifold wikiPageWikiLink Covector.
- Differentiable_manifold wikiPageWikiLink Cover_(topology).
- Differentiable_manifold wikiPageWikiLink Curl_(mathematics).
- Differentiable_manifold wikiPageWikiLink Curve.
- Differentiable_manifold wikiPageWikiLink De_Rham_cohomology.
- Differentiable_manifold wikiPageWikiLink Decision_problem.
- Differentiable_manifold wikiPageWikiLink Definite_bilinear_form.
- Differentiable_manifold wikiPageWikiLink Definite_quadratic_form.
- Differentiable_manifold wikiPageWikiLink Degenerate_bilinear_form.
- Differentiable_manifold wikiPageWikiLink Derivation_(abstract_algebra).
- Differentiable_manifold wikiPageWikiLink Derivation_(differential_algebra).
- Differentiable_manifold wikiPageWikiLink Derivative.
- Differentiable_manifold wikiPageWikiLink Diffeological_space.
- Differentiable_manifold wikiPageWikiLink Diffeology.
- Differentiable_manifold wikiPageWikiLink Diffeomorphism.
- Differentiable_manifold wikiPageWikiLink Diffeomorphisms.
- Differentiable_manifold wikiPageWikiLink Differentiability_class.
- Differentiable_manifold wikiPageWikiLink Differentiable.
- Differentiable_manifold wikiPageWikiLink Differentiable_curve.
- Differentiable_manifold wikiPageWikiLink Differentiable_function.
- Differentiable_manifold wikiPageWikiLink Differential_form.
- Differentiable_manifold wikiPageWikiLink Differential_geometry.
- Differentiable_manifold wikiPageWikiLink Differential_geometry_and_topology.
- Differentiable_manifold wikiPageWikiLink Differential_operator.
- Differentiable_manifold wikiPageWikiLink Differential_structure.
- Differentiable_manifold wikiPageWikiLink Dimension.
- Differentiable_manifold wikiPageWikiLink Direct_sum_of_vector_bundles.
- Differentiable_manifold wikiPageWikiLink Directional_derivative.
- Differentiable_manifold wikiPageWikiLink Divergence.
- Differentiable_manifold wikiPageWikiLink Divergence_theorem.
- Differentiable_manifold wikiPageWikiLink Donaldsons_theorem.
- Differentiable_manifold wikiPageWikiLink Dual_number.
- Differentiable_manifold wikiPageWikiLink Dual_numbers.
- Differentiable_manifold wikiPageWikiLink Dual_space.
- Differentiable_manifold wikiPageWikiLink E8_manifold.
- Differentiable_manifold wikiPageWikiLink Einstein.
- Differentiable_manifold wikiPageWikiLink Embedding.