smooth embedding
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Embedding — In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.When some object X is said to be embedded in another object Y , the embedding is… … Wikipedia
Whitney embedding theorem — In mathematics, particularly in differential topology,there are two Whitney embedding theorems:*The strong Whitney embedding theorem states that any connected smooth m dimensional manifold (required also to be Hausdorff and second countable) can… … Wikipedia
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. Isometric means preserving the length of every path. For instance,… … Wikipedia
Glossary of differential geometry and topology — This is a glossary of terms specific to differential geometry and differential topology. The following two glossaries are closely related: *Glossary of general topology *Glossary of Riemannian and metric geometry.See also: *List of differential… … Wikipedia
Immersion (mathematics) — In mathematics, an immersion is a differentiable map between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M → N is an immersion if:D pf : T p M o T {f(p)}N,is an injective map at every point p of M (where the … Wikipedia
Möbius strip — This article is about the mathematical object. For musical group, see Mobius Band (band). A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having… … Wikipedia
Singular point of a curve — In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied. Contents 1 Algebraic curves in the plane 1.1 … Wikipedia
Solenoid (mathematics) — This page discusses a class of topological groups. For the wrapped loop of wire, see Solenoid. The Smale Williams solenoid. In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse … Wikipedia
Finite type invariant — In the mathematical theory of knots, a finite type invariant is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and… … Wikipedia
Legendrian knot — In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into mathbb R^3, which is tangent to the standard contact structure on mathbb R^3. More generally, Legendrian knots refer to such maps into a contact manifold. ee… … Wikipedia
Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… … Wikipedia
