An integral manifold of a rank-
distribution 
on a manifold 
is an immersed 
-dimensional submanifold 
whose tangent
space satisfies 
at every point 
. Here immersed means that
the inclusion of 
in 
has injective differential, and tangent means that the tangent
space of 
consists exactly of the directions prescribed by the distribution.
An involutive distribution admits local
integral manifolds through every point by the Frobenius
integrability theorem. In the geometry of differential
equations, integral manifolds commonly represent solutions.
Integral Manifold
See also
Cartan Distribution, Differential Equation, Frobenius Integrability Theorem, Involutive Distribution, Manifold, Rank, Submanifold, Tangent SpaceExplore with Wolfram|Alpha
References
Lee, J. M. Introduction to Smooth Manifolds, 2nd ed. New York: Springer, 2012.Cite this as:
Weisstein, Eric W. "Integral Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegralManifold.html