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23 relations: Calculus of variations, Convex set, Covering space, Frame bundle, Gauss map, Holonomic (robotics), Homotopy, Legendrian knot, Mathematics, Metric map, Mikhail Leonidovich Gromov, N-connected space, Nash embedding theorem, Partial differential equation, Pseudoholomorphic curve, Regular homotopy, Robotics, Sphere eversion, Stiefel manifold, Symplectic manifold, Underdetermined system, Winding number, Yakov Eliashberg.
Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Frame bundle
In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex.
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Gauss map
In differential geometry, the Gauss map (named after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S2.
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Holonomic (robotics)
A robot is holonomic if all the constraints that it is subjected to are integrable into positional constraints of the form: The variables q_i are the system coordinates.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Legendrian knot
In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into which is tangent to the standard contact structure on It is the lowest-dimensional case of a Legendrian submanifold, which is an embedding of a k-dimensional manifold into a (2k+1)-dimensional that is always tangent to the contact hyperplane.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Metric map
In the mathematical theory of metric spaces, a metric map is a function between metric spaces that does not increase any distance (such functions are always continuous).
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Mikhail Leonidovich Gromov
Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.
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N-connected space
In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.
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Nash embedding theorem
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Pseudoholomorphic curve
In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation.
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Regular homotopy
In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another.
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Robotics
Robotics is an interdisciplinary branch of engineering and science that includes mechanical engineering, electronics engineering, computer science, and others.
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Sphere eversion
In differential topology, sphere eversion is the process of turning a sphere inside out in a three-dimensional space.
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Stiefel manifold
In mathematics, the Stiefel manifold Vk(Rn) is the set of all orthonormal ''k''-frames in Rn.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Underdetermined system
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns).
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Winding number
In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point.
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Yakov Eliashberg
Yakov Eliashberg (Яков Матвеевич Элиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR.
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References
[1] https://en.wikipedia.org/wiki/Homotopy_principle
