space curves, the Darboux vector is the angular velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it...
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him: Darboux basis Darboux chart Darboux cubic Darboux derivative Darboux equation Darboux frame Darboux integral Darboux net invariants Darboux or Goursat...
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A Darboux basis may refer to: A Darboux basis of a symplectic vector space In differential geometry, a Darboux frame on a surface A Darboux tangent in...
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In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...
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Frenet–Serret formulas (redirect from Unit tangent vector)
momentum of the observer's coordinate system is proportional to the Darboux vector of the frame. Concretely, suppose that the observer carries an (inertial)...
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finite-dimensional symplectic vector space has a basis such that ω {\displaystyle \omega } takes this form, often called a Darboux basis or symplectic basis...
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Gaston Darboux studied the problem of constructing a preferred moving frame on a surface in Euclidean space instead of a curve, the Darboux frame (or...
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The Darboux integral, which is defined by Darboux sums (restricted Riemann sums) yet is equivalent to the Riemann integral. A function is Darboux-integrable...
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The Darboux derivative of a map between a manifold and a Lie group is a variant of the standard derivative. It is arguably a more natural generalization...
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dependent vector field is a construction in vector calculus which generalizes the concept of vector fields. It can be thought of as a vector field which...
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is the standard argument for the modern proof of Darboux's theorem, as well as for the proof of Darboux-Weinstein theorem and other normal form results...
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Contact geometry (section Reeb vector field)
theorem of Darboux, every contact structure on a manifold looks locally like this particular contact structure on the (2n + 1)-dimensional vector space. The...
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Exterior algebra (redirect from Extended vector algebra)
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
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Geodesic curvature (redirect from Geodesic curvature vector)
denotes the second fundamental form. The Gauss–Bonnet theorem. Curvature Darboux frame Gauss–Codazzi equations do Carmo, Manfredo P. (1976), Differential...
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supremum on that subinterval.) The Darboux integral, which is similar to the Riemann integral but based on Darboux sums, is equivalent to the Riemann...
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principal curvatures and principal directions was undertaken by Gaston Darboux, using Darboux frames. The product k1k2 of the two principal curvatures is the...
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and let t = u × T so that T, t, u form an orthonormal basis, called the Darboux frame. The above quantities are related by: ( T ′ t ′ u ′ ) = ( 0 κ g κ...
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Geometric algebra (section Vector space model)
such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in...
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lectures by Charles Hermite (1822–1901), Jules Tannery (1848–1910), Gaston Darboux (1842–1917), Paul Appell (1855–1930), Émile Picard (1856–1941), Édouard...
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Heisenberg group (section On symplectic vector spaces)
{\displaystyle 0\to \mathbf {R} \to H(V)\to V\to 0.} Any symplectic vector space admits a Darboux basis {ej, fk}1 ≤ j,k ≤ n satisfying ω(ej, fk) = δjk and where...
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and symplectic structures. By Darboux's theorem, symplectic manifolds are isomorphic to the standard symplectic vector space locally, hence only have...
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leading geometers devoting themselves to their study.[citation needed] Darboux collected many results in his four-volume treatise Théorie des surfaces...
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of a symplectic vector space is even if it is finite. Darboux theorem Symplectic frame bundle Symplectic spinor bundle Symplectic vector space Maurice de...
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Poisson bi-vector π i j {\displaystyle \pi ^{ij}} is invertible, one has an odd symplectic manifold. In that case, there exists an odd Darboux Theorem....
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precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a...
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partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions...
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joined by Klein two months later. There, they met Camille Jordan and Gaston Darboux. But on 19 July 1870 the Franco-Prussian War began and Klein (who was Prussian)...
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groups of transformations was developed by Sophus Lie and Jean Gaston Darboux, leading to important results in the theory of Lie groups and symplectic...
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primitives of the Darboux derivative. Introduced by Cartan (1904). Subtlety: ( L g ) ∗ X {\displaystyle (L_{g})_{*}X} gives a vector in T g h G if X...
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induces a pairing of odd and even variables. There is a version of the Darboux theorem for P-manifolds, which allows one to equip a P-manifold locally...
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