Invariant solutions of gradient $k$-Yamabe solitons

TL;DR

This paper classifies and constructs explicit examples of gradient k-Yamabe solitons conformal to pseudo-Euclidean space, focusing on invariant solutions under translation and rotation, including those with null curvatures.

Contribution

It provides a complete classification of invariant gradient k-Yamabe solitons and constructs infinitely many explicit geodesically complete examples.

Findings

Classification of translation-invariant solitons

Classification of rotational invariant solitons with null curvatures

Construction of explicit steady gradient k-Yamabe solitons

Abstract

The purpose of this paper is to study gradient $k$-Yamabe solitons conformal to pseudo-Euclidean space. We characterize all such solitons invariant under the action of an $(n-1)$-dimensional translation group. For rotational invariant solutions, we provide the classification of solitons with null curvatures. As an application, we construct infinitely many explicit examples of geodesically complete steady gradient $k$-Yamabe solitons conformal to the Lorentzian space.