Approximation of Regular Sasakian Manifolds

TL;DR

This paper demonstrates that all compact regular Sasakian manifolds can be approximated by CR immersions into spheres, and extends the approximation to certain non-compact manifolds, providing new insights into their geometric structure.

Contribution

The paper proves the universal approximation of compact regular Sasakian manifolds by CR immersions into spheres and extends results to non-compact η-Einstein manifolds.

Findings

All compact regular Sasakian manifolds can be CR immersed into a sphere.

Non-compact η-Einstein manifolds can be approximated via immersions into infinite dimensional spheres.

Several explicit examples illustrate the approximation results.

Abstract

We investigate the problem of approximating a regular Sasakian structure by CR immersions in a standard sphere. Namely, we show that this is always possible for compact Sasakian manifolds. Moreover, we prove an approximation result for non-compact $\eta$-Einstein manifolds via immersions in the infinite dimensional sphere. We complement this with several examples.