Submanifold example sentences

"Submanifold" Example Sentences

1. The submanifold of a complex manifold is a complex submanifold.
2. The submanifold can have any dimension, from zero to the dimension of the original manifold.
3. A submanifold is a subset of a manifold that has a different dimension than the original manifold.
4. The submanifold is a subset of the original manifold, but with a different dimension.
5. A submanifold is a subset of a manifold which has a lower dimension than the original manifold.
6. A submanifold is a subset of a manifold which is defined as having a lower dimension than the original manifold.
7. A submanifold is a subset of a manifold which is of lower dimension than the original manifold.
8. A submanifold is a subset of a manifold which is of lower dimension than the original manifold, and is itself a manifold.
9. Submanifolds can be embedded in a larger manifold, or they can be self-contained.
10. Submanifolds are usually defined as a subset of a larger manifold, but they can also be self-contained.
11. Submanifolds can be of any dimension, from zero to the dimension of the original manifold.
12. Submanifolds can be embedded in a larger manifold, or they can also be self-contained.
13. Submanifolds can be of any dimension, from zero to the dimension of the original manifold, and can have any number of components.
14. Submanifolds can be embedded in a larger manifold, or they can also be self-contained, and can have any number of components.
15. Submanifolds can be embedded in a larger manifold, or they can also be self-contained, and can have any number of components, depending on the particular submanifold.
16. Submanifolds can be embedded in a larger manifold, or they can also be self-contained, and can have any number of components, depending on the particular submanifold and its dimension.
17. Submanifolds can have different properties than the larger manifold they are embedded in, such as curvature and torsion.
18. Submanifolds can also have different topological properties than the larger manifold they are embedded in.
19. Submanifolds can be used to study the geometry and topology of a larger manifold.
20. Submanifolds can be used to study the geometry and topology of a larger manifold, and can also be used to study the properties of the manifold itself.

Common Phases

Tangent bundle; Cotangent bundle; Symplectic manifold; Lagrangian submanifold; Riemannian submanifold; Hermitian submanifold; Kähler submanifold; Special Lagrangian submanifold