A differentiable map f:XY differential manifolds X and Y is called a submersionMathworldPlanetmath at a point xX if the tangent map


between the tangent spacesPlanetmathPlanetmath of X and Y at x and f(x) is surjective.

If f is a submersion at every point of X, then f is called a submersion. A submersion f:XY is an open mapping, and its image is an open submanifold of Y.

A fibre bundle p:XB over a manifold B is an example of a submersion.

Title submersion
Canonical name Submersion
Date of creation 2013-03-22 15:28:49
Last modified on 2013-03-22 15:28:49
Owner pbruin (1001)
Last modified by pbruin (1001)
Numerical id 4
Author pbruin (1001)
Entry type Definition
Classification msc 53-00
Classification msc 57R50
Related topic Immersion