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...

him: Darboux basis Darboux chart Darboux cubic Darboux derivative Darboux equation Darboux frame Darboux integral Darboux net invariants Darboux or Goursat...

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...

momentum of the observer's coordinate system is proportional to the Darboux vector of the frame. Concretely, suppose that the observer carries an (inertial)...

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...

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...

finite-dimensional symplectic vector space has a basis such that ω {\displaystyle \omega } takes this form, often called a Darboux basis or symplectic basis...

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...

The Darboux integral, which is defined by Darboux sums (restricted Riemann sums) yet is equivalent to the Riemann integral. A function is Darboux-integrable...

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...

theorem of Darboux, every contact structure on a manifold looks locally like this particular contact structure on the (2n + 1)-dimensional vector space. The...

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...

supremum on that subinterval.) The Darboux integral, which is similar to the Riemann integral but based on Darboux sums, is equivalent to the Riemann...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in...

principal curvatures and principal directions was undertaken by Gaston Darboux, using Darboux frames. The product k1k2 of the two principal curvatures is the...

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...

denotes the second fundamental form. The Gauss–Bonnet theorem. Curvature Darboux frame Gauss–Codazzi equations do Carmo, Manfredo P. (1976), Differential...

were contributed subsequently by Lagrange, Liouville, Laplace, Jacobi, Darboux,[citation needed] Le Verrier, Velde,[citation needed] Hamilton, Poincaré...

groups of transformations was developed by Sophus Lie and Jean Gaston Darboux, leading to important results in the theory of Lie groups and symplectic...

{\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...

lectures by Charles Hermite (1822–1901), Jules Tannery (1848–1910), Gaston Darboux (1842–1917), Paul Appell (1855–1930), Émile Picard (1856–1941), Édouard...

of a symplectic vector space is even if it is finite. Darboux theorem Symplectic frame bundle Symplectic spinor bundle Symplectic vector space Maurice de...

theorem Myers theorem Gromov's compactness theorem Gauss–Codazzi equations Darboux frame Hypersurface Induced metric Nash embedding theorem minimal surface...

leading geometers devoting themselves to their study.[citation needed] Darboux collected many results in his four-volume treatise Théorie des surfaces...

and symplectic structures. By Darboux's theorem, symplectic manifolds are isomorphic to the standard symplectic vector space locally, hence only have...

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...

partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions...

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...

Law", too. Lagrange, Joseph-Louis (1869) [1776]. Serret, Joseph-Alfred; Darboux, Jean-Gaston (eds.). "Sur l'attraction des sphéroïdes elliptiques" [On...