An integral manifold of a rank-
distribution 
on a manifold 
is an immersed 
-dimensional submanifold 
whose tangent
space satisfies 
at every point 
. Thus an integral manifold is everywhere tangent to the
prescribed directions. 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, SubmanifoldExplore 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