totally real submanifold


Suppose that MN 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 (, 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 Txc(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.


  • 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