## Manifold

In mathematics, a **manifold** of dimension *n* is a topological space that near each point resembles *n*-dimensional Euclidean space. More precisely, each point of an *n*-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension *n*. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.

Read more about Manifold.

### Some articles on manifold:

... The Whitehead

**manifold**is an example of a 3-

**manifold**that is contractible but not simply connected at infinity ... property is invariant under homeomorphism, this proves that the Whitehead

**manifold**is not homeomorphic to R3 ... However, it is a theorem that any contractible n-

**manifold**which is also simply connected at infinity is homeomorphic to Rn ...

... Suppose is a Riemannian

**manifold**and ... some function such that for all and all then is constant, and the

**manifold**has constant sectional curvature (also known as a space form when is complete) the Ricci ...

**Manifold**

... In Riemannian geometry, a collapsing or collapsed

**manifold**is an n-dimensional

**manifold**M that admits a sequence of Riemannian metrics gn, such that as n goes to infinity the

**manifold**is ... The simplest example is a flat

**manifold**, whose metric can be rescaled by 1/n, so that the

**manifold**is close to a point, but its curvature remains 0 for all n ...

**Manifold**s - Centrality of

**Manifold**s

... Why does one study

**manifolds**?

**Manifolds**, and generalized spaces composed of

**manifolds**such as stratified spaces, occupy a central role in topology ... can be stratified into

**manifold**pieces), and that they are the space "modeled on" Euclidean space (a space that looks locally like Euclidean space) – i.e ...

**Manifolds**are homogeneous and tame (locally isomorphic to Euclidean space) in this manner, and one may ask if all "tame" homogeneous spaces are

**manifolds**, or whether there is a natural class where more ...

... the collision occurs into a collision

**manifold**, the phase space point is cut out and in its place a smooth

**manifold**is pasted ... McGehee then went on to study the flow on the collision

**manifold**...

### More definitions of "manifold":

- (
*noun*): A pipe that has several lateral outlets to or from other pipes.

- (
*adj*): Many and varied; having many features or forms.

Example:*"Manifold reasons"; "our manifold failings"; "manifold intelligence"*

Synonyms: multiplex

- (
*noun*): A lightweight paper used with carbon paper to make multiple copies.

Synonyms: manifold paper

- (
*noun*): A set of points such as those of a closed surface or and analogue in three or more dimensions.

- (
*verb*): Combine or increase by multiplication.

Synonyms: multiply

### Famous quotes containing the word manifold:

“Thy love is such I can no way repay,

The heavens reward thee *manifold* I pray.

Then while we live, in love lets so persever,

That when we live no more, we may live ever.”

—Anne Bradstreet (c. 1612–1672)

“The Lord wrote it all down on the little slate

Of the baby tortoise.

Outward and visible indication of the plan within,

The complex, *manifold* involvedness of an individual creature”

—D.H. (David Herbert)

“Odysseus saw the sirens; they were charming,

Blonde, with snub breasts and little neat posteriors,”

—John Streeter *Manifold* (b. 1915)