$\eta$-Einstein Sasakian immersions in non-compact Sasakian space forms

TL;DR

This paper classifies complete regular $ ext{eta}$-Einstein Sasakian manifolds that can be immersed into the Heisenberg group or a product of a ball with a real line, expanding understanding of their geometric structures.

Contribution

It provides a complete classification of $ ext{eta}$-Einstein Sasakian manifolds immersible into specific non-compact Sasakian space forms.

Findings

Classification of $ ext{eta}$-Einstein Sasakian manifolds in the non-compact case

Characterization of immersions into the Heisenberg group and $ ext{B}^N imes ext{R}$

Conditions for the existence of such immersions

Abstract

The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into $ \mathbb{B}^N\times \mathbb{R}$ equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the $\eta$-Einstein case.