DBpedia – Linked Data Fragments

Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Metric_tensor> ?p ?o }

• Metric_tensor abstract "In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space. In the same way as a dot product, metric tensors are used to define the length of, and angle between, tangent vectors.A metric tensor is called positive-definite if it assigns a positive value to every nonzero vector. A manifold equipped with a positive-definite metric tensor is known as a Riemannian manifold. By integration, the metric tensor allows one to define and compute the length of curves on the manifold. The curve connecting two points that (locally) has the smallest length is called a geodesic, and its length is the distance that a passenger in the manifold needs to traverse to go from one point to the other. Equipped with this notion of length, a Riemannian manifold is a metric space, meaning that it has a distance function d(p,q) whose value at a pair of points p and q is the distance from p to q. Conversely, the metric tensor itself is the derivative of the distance function (taken in a suitable manner). Thus the metric tensor gives the infinitesimal distance on the manifold.While the notion of a metric tensor was known in some sense to mathematicians such as Carl Gauss from the early 19th century, it was not until the early 20th century that its properties as a tensor were understood by, in particular, Gregorio Ricci-Curbastro and Tullio Levi-Civita, who first codified the notion of a tensor. The metric tensor is an example of a tensor field.With a holonomic basis on the manifold, a metric tensor takes on the form of a symmetric matrix whose entries transform covariantly under changes to the coordinate system. Thus a metric tensor is a covariant symmetric tensor. From the coordinate-independent point of view, a metric tensor is defined to be a nondegenerate symmetric bilinear form on each tangent space that varies smoothly from point to point.".
• Metric_tensor wikiPageExternalLink index.php?id=11&PPN=PPN235181684_0054&DMDID=DMDLOG_0011&L=1.
• Metric_tensor wikiPageExternalLink digbib.cgi?PPN35283028X_0006_2NS.
• Metric_tensor wikiPageID "195795".
• Metric_tensor wikiPageLength "51876".
• Metric_tensor wikiPageOutDegree "227".
• Metric_tensor wikiPageRevisionID "675191381".
• Metric_tensor wikiPageWikiLink Analytic_function.
• Metric_tensor wikiPageWikiLink Angle.
• Metric_tensor wikiPageWikiLink Arc_length.
• Metric_tensor wikiPageWikiLink Arclength.
• Metric_tensor wikiPageWikiLink Area.
• Metric_tensor wikiPageWikiLink Basic_introduction_to_the_mathematics_of_curved_spacetime.
• Metric_tensor wikiPageWikiLink Basis_(linear_algebra).
• Metric_tensor wikiPageWikiLink Basis_of_a_vector_space.
• Metric_tensor wikiPageWikiLink Bilinear_form.
• Metric_tensor wikiPageWikiLink Bilinear_transform.
• Metric_tensor wikiPageWikiLink Black_hole.
• Metric_tensor wikiPageWikiLink Borel_measure.
• Metric_tensor wikiPageWikiLink Carl_Friedrich_Gauss.
• Metric_tensor wikiPageWikiLink Carl_Gauss.
• Metric_tensor wikiPageWikiLink Cartesian_coordinate_system.
• Metric_tensor wikiPageWikiLink Cartesian_coordinates.
• Metric_tensor wikiPageWikiLink Cartesian_space.
• Metric_tensor wikiPageWikiLink Category:Concepts_in_physics.
• Metric_tensor wikiPageWikiLink Category:Differential_geometry.
• Metric_tensor wikiPageWikiLink Category:Metric_tensors.
• Metric_tensor wikiPageWikiLink Category:Riemannian_geometry.
• Metric_tensor wikiPageWikiLink Category:Tensors.
• Metric_tensor wikiPageWikiLink Chain_rule.
• Metric_tensor wikiPageWikiLink Change_of_basis.
• Metric_tensor wikiPageWikiLink Classical_mechanics.
• Metric_tensor wikiPageWikiLink Clifford_algebra.
• Metric_tensor wikiPageWikiLink Column_vector.
• Metric_tensor wikiPageWikiLink Compact_support.
• Metric_tensor wikiPageWikiLink Connected_space.
• Metric_tensor wikiPageWikiLink Constant_function.
• Metric_tensor wikiPageWikiLink Continuous_function.
• Metric_tensor wikiPageWikiLink Continuously_differentiable.
• Metric_tensor wikiPageWikiLink Coordinate-free.
• Metric_tensor wikiPageWikiLink Coordinate_chart.
• Metric_tensor wikiPageWikiLink Coordinate_differential.
• Metric_tensor wikiPageWikiLink Coordinate_vector.
• Metric_tensor wikiPageWikiLink Cotangent_bundle.
• Metric_tensor wikiPageWikiLink Covariance_and_contravariance_of_vectors.
• Metric_tensor wikiPageWikiLink Covector.
• Metric_tensor wikiPageWikiLink Cross_product.
• Metric_tensor wikiPageWikiLink Definite_bilinear_form.
• Metric_tensor wikiPageWikiLink Definite_quadratic_form.
• Metric_tensor wikiPageWikiLink Degeneracy_(mathematics).
• Metric_tensor wikiPageWikiLink Degenerate_bilinear_form.
• Metric_tensor wikiPageWikiLink Derivative.
• Metric_tensor wikiPageWikiLink Determinant.
• Metric_tensor wikiPageWikiLink Differentiable_function.
• Metric_tensor wikiPageWikiLink Differentiable_manifold.
• Metric_tensor wikiPageWikiLink Differential_(infinitesimal).
• Metric_tensor wikiPageWikiLink Differential_form.
• Metric_tensor wikiPageWikiLink Differential_geometry.
• Metric_tensor wikiPageWikiLink Dot_product.
• Metric_tensor wikiPageWikiLink Double_dual.
• Metric_tensor wikiPageWikiLink Dual_basis.
• Metric_tensor wikiPageWikiLink Dual_space.
• Metric_tensor wikiPageWikiLink Eigenvalue.
• Metric_tensor wikiPageWikiLink Eigenvalues_and_eigenvectors.
• Metric_tensor wikiPageWikiLink Euclidean_distance.
• Metric_tensor wikiPageWikiLink Euclidean_geometry.
• Metric_tensor wikiPageWikiLink Euclidean_space.
• Metric_tensor wikiPageWikiLink Euclidean_vector.
• Metric_tensor wikiPageWikiLink Exterior_algebra.
• Metric_tensor wikiPageWikiLink Exterior_product.
• Metric_tensor wikiPageWikiLink Fiber_bundle.
• Metric_tensor wikiPageWikiLink Fiber_product.
• Metric_tensor wikiPageWikiLink Finsler_manifold.
• Metric_tensor wikiPageWikiLink First_fundamental_form.
• Metric_tensor wikiPageWikiLink Frame_bundle.
• Metric_tensor wikiPageWikiLink Geodesic.
• Metric_tensor wikiPageWikiLink Geodesic_equation.
• Metric_tensor wikiPageWikiLink Graduate_Studies_in_Mathematics.
• Metric_tensor wikiPageWikiLink Gravitational_constant.
• Metric_tensor wikiPageWikiLink Gregorio_Ricci-Curbastro.
• Metric_tensor wikiPageWikiLink Holonomic_basis.
• Metric_tensor wikiPageWikiLink Hypersurface.
• Metric_tensor wikiPageWikiLink Identically_zero.
• Metric_tensor wikiPageWikiLink Immersed_submanifold.
• Metric_tensor wikiPageWikiLink Immersion_(mathematics).
• Metric_tensor wikiPageWikiLink Injective.
• Metric_tensor wikiPageWikiLink Injective_function.
• Metric_tensor wikiPageWikiLink Integral.
• Metric_tensor wikiPageWikiLink Integration_by_substitution.
• Metric_tensor wikiPageWikiLink Interval_(mathematics).
• Metric_tensor wikiPageWikiLink Introduction_to_the_mathematics_of_general_relativity.
• Metric_tensor wikiPageWikiLink Inverse_matrix.
• Metric_tensor wikiPageWikiLink Invertible_matrix.
• Metric_tensor wikiPageWikiLink Jacobian_matrix.
• Metric_tensor wikiPageWikiLink Jacobian_matrix_and_determinant.
• Metric_tensor wikiPageWikiLink Kernel_(set_theory).
• Metric_tensor wikiPageWikiLink Kinetic_energy.
• Metric_tensor wikiPageWikiLink Kronecker_delta.
• Metric_tensor wikiPageWikiLink Lagranges_identity.
• Metric_tensor wikiPageWikiLink Lebesgue_integral.

• next