Generalized quasi Yamabe gradient solitons

TL;DR

This paper characterizes the structure of complete generalized quasi Yamabe gradient solitons, showing they are essentially quasi Yamabe solitons or have a warped product form, revealing their geometric nature.

Contribution

It proves that nontrivial complete generalized quasi Yamabe gradient solitons are either quasi Yamabe solitons or have a warped product structure, clarifying their geometric classification.

Findings

Complete generalized quasi Yamabe gradient solitons are quasi Yamabe solitons on each component.

Locally conformally at generalized quasi Yamabe solitons have a warped product structure.

Provides a geometric classification of these solitons.

Abstract

We prove that a nontrivial complete generalized quasi Yamabe gradient soliton (M; g) must be a quasi Yamabe gradient soliton on each connected component of M and that a nontrivial complete locally conformally at generalized quasi Yamabe gradient soliton has a special warped product structure.