Research ArticleNo Access

Conformal vector fields and Yamabe solitons

Nasser Bin Turki

Department of Mathematics, College of Science, King Saud University, P. O. Box-2455 Riyadh-11451, Saudi Arabia

E-mail Address: nassert@ksu.edu.sa

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Bang-Yen Chen

http://orcid.org/0000-0002-1270-094X

Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lancing, Michigan 48824-1027, USA

E-mail Address: chenb@msu.edu

Corresponding author.

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, and

Sharief Deshmukh

Department of Mathematics, College of Science, King Saud University, P. O. Box-2455 Riyadh-11451, Saudi Arabia

E-mail Address: shariefd@ksu.edu.sa

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https://doi.org/10.1142/S0219887819500531Cited by:3 (Source: Crossref)

Abstract

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several sufficient conditions on the soliton vector fields of Yamabe solitons under which their metrics are Yamabe metrics.

Keywords:

AMSC: 53C21, 35C06, 35J62

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