ABSTRACT
The second differential of F at the point z0 is negative semidefinite. A straightforward calculation yields:
~ a,[j(zo) aJ:(ZJ ( . )( . ) + £...J a a-tk + ltk+n tj - ltj+n .. k -I Zk ZJ· l,); -
where t E JR2n \ {0} with I, t/J.i = 0 . If we set wj = tj + itj+n, with i=l
Lemma 7 .2d has several interesting geometric consequences which are discussed in [ 67 ], and which we briefly discuss. Recall that iff is locally biholomrphic at z0 , then there exists a neighborhood V of z0 for which f is a biholomorphic mapping between V and f(V). If we let M denote the
intersection V and { z E en : II z II = r0 } , then f(M) is a real hypersurface. Since
is an outer normal vector to f(M) at the point f(z0 ), from part (i) of the
satisfy:
inequalities.
