Gradient Yamabe Solitons on Multiply Warped Product Manifolds

Abstract

We consider gradient Yamabe solitons on multiply warped product manifolds. We find the necessary and sufficient conditions for multiply warped product manifolds to be gradient Yamabe solitons.

On WARPED PRODUCT MANIFOLDS ADMITTING Τ-Quasi RICCI-HARMONIC METRICS

“…In [17], the authors studied a structure such that the warping function and the potential function are not the same. This idea provided interesting results and led a growing interest in warped products on Ricci solitons [1,5,6,8,11,13,17], almost Ricci solitons [7], Yamabe solitons [10,19] and RH solitons [2].…”

Study on Twisted Product Almost Gradient Yamabe Solitons

“…In 2011, Cao and two coauthors [3] studied classification theorems for complete nontrivial locally conformally flat gradient Yamabe soliton. In [9], they found sufficient conditions on the soliton vector field under which the metric of a Yamabe soliton is a Yamabe metric, that is, a metric of constant scalar curvature. Moreover, in [8], we can see the various examples of compact and noncompact almost gradient Yamabe soliton.…”

“…e present authors [4] studied gradient Yamabe soliton in the warped product manifolds and admittance of gradient Yamabe solitons and geometric structures for some model spaces. In 2019, Karaca [9] obtained a classification theorem regarding a gradient Yamabe soliton on multiplying warped product space with splitting potential function. With respect to the result, we obtain similar classification theorems for the warped product or the twisted product space with almost gradient Yamabe soliton.…”

“…Especially considering the condition of the conformal flatness, the classification and characterizations of the space were greatly helped. In addition to these, there are many works on solitons on the twisted product spaces [10][11][12][13][14] and Yamabe solitons [2,[5][6][7][8][9].…”

A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds

“…To understand the existence of gradient Yamabe solitons one can see the paper [4]. Also, Gradient Yamabe solitons have been investigated by several authors such as ( [1], [2], [3], [7], [11], [15]) and many others. In [10], Hsu proved that for dimension n ≥ 3, the metric of any compact Yamabe gradient soliton (M n , g) is of constant scalar curvature.…”