totally real submanifold
Definition.
Suppose that is a CR submanifold. If the CR dimension of is 0, we say that is totally real. If in addition is generic (http://planetmath.org/GenericManifold), then is said to be maximally totally real (or sometimes just maximally real).
Note that if is maximally totally real, then the real dimension is automatically , this is because (the complex tangent space) is of dimension 0, and thus must be of real dimension if is to be a generic manifold.
References
- 1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999.