On The Non-Existence of CR-Regular Embeddings of $S^5$

TL;DR

This paper proves that it is impossible to embed the 5-sphere into four-dimensional complex space in a CR-regular manner, extending the non-existence results to higher-dimensional spheres as well.

Contribution

It establishes the non-existence of CR-regular embeddings of $S^5$ into $ extbf{C}^4$, providing new insights into the embedding theory of spheres in complex spaces.

Findings

No CR-regular embedding of $S^5$ into $ extbf{C}^4$ exists.

Analogous non-existence results for higher-dimensional spheres.

Contributes to understanding constraints on sphere embeddings in complex geometry.

Abstract

In this article, we show that there exists no CR-regular embedding of the 5-sphere $S^5$ into $\mathbb{C}^4$, and also obtain analogous results for embeddings of higher dimensional spheres into complex space.