Submersion
A submersion is a smooth map f:M->N when
| dimM>=dimN, |
given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the canonical submersion alpha of R^n onto R^k when n>=k,
| alpha(x_1,...,x_n)=(x_1,...,x_k). |
In fact, if f is a submersion, then it is possible to find coordinates around x in M and coordinates around f(x) in N such that f is the canonical submersion written in these coordinates. For example, consider the submersion of R^2-{(0,0)} onto the circle S^1, given by f(x,y)=(x,y)/sqrt(x^2+y^2).
See also
ImmersionThis entry contributed by Todd Rowland
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Rowland, Todd. "Submersion." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Submersion.html