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单词 TotallyRealSubmanifold
释义

totally real submanifold


Definition.

Suppose that MN is a CR submanifold. If the CR dimension of M is 0, we say that M is totally real. If in additionM 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 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.

References

  • 1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999.
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