THE ENVELOPE OF HOLOMORPHY OF A TWO-MANIFOLD IN C2 61
of a fc-manifold in C", k>ιι, with a one-higher dimensional envelope
of holomorphy. For real codimension 2, all such embeddings have this
property. One could conjecture that:
a) All compact submanifolds of C", of real dimension > n, have an
envelope of holomorphy of at least one higher dimension.
b) All compactsubmanifoldsofC",ofrealdimension «,have an envelope
of holomorphy of at least one higher dimension, provided that the mani-
folds are not totally real.
It is possible that the results mentioned in Remark No. 3 will be applicable
in proving a) for five-dimensional submanifolds of C4.
Added in Proof: S. Greenfield has recently given an affirmative an-
swer to the question in Remark 2.
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