Rigity results on $\rho$-Einstein solitons with zero scalar curvature

TL;DR

This paper proves that certain $ ho$-Einstein solitons conformal to pseudo-Euclidean space with zero scalar curvature are necessarily steady and flat, providing an explicit example related to Kazdan's question.

Contribution

It establishes rigidity results for $ ho$-Einstein solitons under specific symmetry and curvature conditions, and offers an explicit example addressing a known open question.

Findings

Such solitons are necessarily steady and flat.

Provides an explicit example related to Kazdan's question.

Enhances understanding of $ ho$-Einstein solitons with zero scalar curvature.

Abstract

In this paper we show that a $\rho$-Einstein solitons conformal to a pseudo-Euclidean space, invariant under the action of the pseudo-orthogonal group with zero scalar curvature is stady and consequently flat. How application of the results obtained we present an explicit example for a the question proposed by Kazdan in [17].