totally real submanifold
Definition.
Suppose that M⊂ℂN is a CR submanifold. If the CR dimension of M is 0, we say that M is totally real. If in addition M is generic (http://planetmath.org/GenericManifold), then M is said to be maximally totally real (or sometimes just maximally real).
Note that if M is maximally totally real, then the real dimension is automatically N, this is because Tcx(M)=Tx(M)∩JTx(M) (the complex tangent space) is of dimension 0, and thus Tx(M) must be of real dimension N if M is to be a generic manifold.
References
- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
Title | totally real submanifold |
Canonical name | TotallyRealSubmanifold |
Date of creation | 2013-03-22 14:56:05 |
Last modified on | 2013-03-22 14:56:05 |
Owner | jirka (4157) |
Last modified by | jirka (4157) |
Numerical id | 5 |
Author | jirka (4157) |
Entry type | Definition |
Classification | msc 32V05 |
Synonym | totally real manifold |
Related topic | CRSubmanifold |
Related topic | GenericManifold |
Defines | maximally totally real submanifold |
Defines | maximally totally real manifold |
Defines | maximally real manifold |