### A holomorphic representation formula for parabolic hyperspheres

A holomorphic representation formula for special parabolic hyperspheres is given.

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A holomorphic representation formula for special parabolic hyperspheres is given.

We construct closed complex submanifolds of ${\u2102}^{n}$ which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of ${\u2102}^{n}$.

In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold $X$, with 1- dimensional exceptional set $S$ and finitely generated second homology group ${H}_{2}(X,\mathbb{Z})$, is embeddable in ${\u2102}^{m}\times \u2102{\mathbb{P}}_{n}$ if and only if $X$ is Kähler, and this case occurs only when $S$ does not contain any effective curve which is a boundary.

We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.