An Extension Theorem for Real Kahler Submanifolds in Codimension Four

Jinwen Yan; Fangyang Zheng

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arXiv · 1210.3772

An Extension Theorem for Real Kahler Submanifolds in Codimension Four

Jinwen Yan·Fangyang Zheng

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Abstract

In this article, we prove a Kahler extension theorem for real Kahler submanifolds of codimension 4 and rank at least 5. Our main theorem states that such a manifold is a holomorphic hypersurface in another real Kahler submanifold of codimension 2. This generalizes a result of Dajczer and Gromoll in 1997 which states that any real Kahler submanifolds of codimension 3 and rank at least 4 admits a Kahler extension.

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Jinwen Yan, Fangyang Zheng. 2012-10-14. An Extension Theorem for Real Kahler Submanifolds in Codimension Four. https://arxiv.org/abs/1210.3772

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