On gradient Ricci solitons and Yamabe solitons

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

1. Introduction

2. Harmonic curvature in warped product spaces M = R × f F

3. Gradient Ricci soliton in M = R × f F

4. Gradient Ricci soliton in M = B × f F

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