On Einstein hypersurfaces of a remarkable class of Sasakian manifolds

TL;DR

This paper proves that complete Einstein hypersurfaces tangent to the Reeb vector field cannot exist in certain regular Sasakian manifolds that fiber onto complex Stein manifolds.

Contribution

It provides a non-existence theorem for a specific class of Einstein hypersurfaces in regular Sasakian manifolds, expanding understanding of geometric structures.

Findings

No complete Einstein hypersurfaces tangent to the Reeb vector field exist in the specified setting.

The result applies to Sasakian manifolds fibered onto complex Stein manifolds.

Advances the classification of Einstein hypersurfaces in Sasakian geometry.

Abstract

We present a non existence result of complete, Einstein hypersurfaces tangent to the Reeb vector field of a regular Sasakian manifold which fibers onto a complex Stein manifold.