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arXiv · 1811.11526

Kaehler submanifolds of hyperbolic space

Marcos Dajczer·Theodoros Vlachos
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Abstract

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

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Marcos Dajczer, Theodoros Vlachos. 2018-11-28. Kaehler submanifolds of hyperbolic space. https://arxiv.org/abs/1811.11526

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