Ads
related to: three dimensional manifolds and marine parts for sale on craigslist
Search results
Results from the WOW.Com Content Network
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer ...
4.3 Infinite-dimensional manifolds. 5 See also. 6 References. ... Spherical 3-manifold; Special classes of Riemannian manifolds. Einstein manifold. Ricci-flat manifold;
Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds).
Ian Agol [needs IPA] (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. [2] Education and career
There is a unique connected 0-dimensional manifold, namely the point, and disconnected 0-dimensional manifolds are just discrete sets, classified by cardinality. They have no geometry, and their study is combinatorics. A connected compact 1-dimensional manifold without boundary is homeomorphic (or diffeomorphic if it is smooth) to the circle.
Once a small subfield of geometric topology, the theory of 3-manifolds has experienced tremendous growth in the latter half of the 20th century. The methods used tend to be quite specific to three dimensions, since different phenomena occur for 4-manifolds and higher dimensions.
Ads
related to: three dimensional manifolds and marine parts for sale on craigslist