Abstract
We present several local and global results on isometric immersions of Kaehler manifolds M 2 n M^{2n} into hyperbolic space H 2 n + p \mathbb {H}^{2n+p} . For instance, a classification is given in the case of dimension n ≥ 4 n\geq 4 and codimension p = 2 p=2 . Moreover, as corollaries of general results, we conclude that there are no isometric immersions in codimension p ≤ n − 2 p\leq n-2 if the Kaehler manifold is of dimension n ≥ 4 n\geq 4 and either has a point of positive holomorphic sectional curvature or is compact.
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