Sentence examples for be an integrable distribution from inspiring English sources

Let ((M,g,S TM))) be a ((2n+r))-dimensional r-lightlike submanifold and (S TM)) be an integrable distribution.

Let ((M,g,S TM))) be an ((n+r))-dimensional r-lightlike submanifold of semi-Riemannian manifold and (S TM)) be an integrable distribution of index q.

Let ((M,g,S TM))) be an ((r+3))-dimensional r-lightlike submanifold of a semi-Riemannian manifold and (S TM)) be an integrable distribution.

Let ((M,g,S TM))) be an ((n+r))-dimensional r-lightlike submanifold and (S TM)) be an integrable distribution of index q.

Let ((M,g,S TM))) be an ((n+r))-dimensional r-lightlike submanifold of a semi-Riemannian manifold and (S TM)) be an integrable distribution of index q.

Let ((M,g,S TM))) be an ((n+r))-dimensional r-lightlike submanifold of an m̃-dimensional semi-Riemannian manifold of index ((q+tilde{q})) and (S TM)) be an integrable distribution.

Thus, D o is an integrable distribution.

The screen distribution S ( T M ) is an integrable distribution.

This implies that [ U, V ] ∈ Γ ( D α ) and D α is an integrable distribution.

Then the following assertions are equivalent: (1) The screen distribution S ( T M ) is an integrable distribution.

Just as in the well-known case of locally product Riemannian or semi-Riemannian manifolds [2 4, 7], if S ( T M ) is an integrable distribution, then M is locally a product manifold M = C 1 × M ∗, where C 1 is a null curve tangent to Rad ( T M ), and M ∗ is a leaf of the integrable screen distribution S ( T M ).