Remarks on Some Soliton Types with Certain Vector Fields

Abstract

This paper mainly aims to investigate some soliton kinds with certain vector fields on Riemannian manifolds and gives some notable geometric results as regards such vector fields. Also, in this paper some special tensors that have an important place in Riemannian geometry are discussed and given some significant links between these tensors. Finally, an example that supports one of our results is given.

Keywords

• Ricci soliton
• Yamabe soliton
• Conformal quadratic Killing tensor
• $\mathcal{Z}$-curvature tensor.

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