submanifold
Look at other dictionaries:
Submanifold — In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S rarr; M satisfies certain properties. There are different types of submanifolds depending on exactly which … Wikipedia
Riemannian submanifold — A Riemannian submanifold N of a Riemannian manifold M is a smooth manifoldequipped with the induced Riemannian metric from M . The image of an isometric immersion is a Riemannian submanifold … Wikipedia
Taut submanifold — In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that every distance function for which is a Morse function, is perfect. If N is not compact, one needs to consider the restriction of the… … Wikipedia
JSJ decomposition — In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: Irreducible orientable closed (i.e., compact and without boundary) 3 manifolds have a unique (up to isotopy)… … Wikipedia
Symplectic cut — In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that… … Wikipedia
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. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… … Wikipedia
Connected sum — In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the… … 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
Transversality — in mathematics is a notion that describes how spaces can intersect; transversality can be seen as the opposite of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is… … Wikipedia
Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… … Wikipedia
