# Category: Maps of manifolds

Connection (principal bundle)
In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fiber
Riemannian submersion
In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projectio
Sobolev mapping
In mathematics, a Sobolev mapping is a mapping between manifolds which has smoothness in some sense. Sobolev mappings appear naturally in manifold-constrained problems in the calculus of variations an
Homotopy
In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós "same, similar" and τόπος tópos "place") if on
Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential (or pushforward) is everywhere injective. Explicitly, f : M → N is an immersion if is an i
Ambient isotopy
In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another s
Topological rigidity
In the mathematical field of topology, a manifold M is called topologically rigid if every manifold homotopically equivalent to M is also homeomorphic to M.
Maps of manifolds
In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed
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 is said to be embedde
Connection (fibred manifold)
In differential geometry, a fibered manifold is surjective submersion of smooth manifolds Y → X. Locally trivial fibered manifolds are fiber bundles. Therefore, a notion of connection on fibered manif
Affine connection
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were
Submersion (mathematics)
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept in differential topology. The notion of a sub
Cartan connection
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general c
Connection form
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, c