On the construction of gradient Ricci soliton warped product

Abstract

In this paper we show that an expanding or steady gradient Ricci soliton warped product $B^n{\times }_f{F}^m$, $m>1$, whose warping function $f$ reaches both maximum and minimum must be a Riemannian product. Moreover, we present a necessary and sufficient condition for constructing a gradient Ricci soliton warped product. As an application, we present a class of expanding Ricci soliton warped product having as a fiber an Einstein manifold with non-positive scalar curvature. We also discuss some obstructions to this construction, especially in the case when the base of the warped product is compact.

Final version. To appear in Journal of Nonlinear Analysis

References in corpus (2)

• Some New Examples of Non-Kähler Ricci Solitons
• Special Kähler-Ricci potentials and Ricci solitons

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• A note on gradient Ricci soliton warped metrics
• Geometric and analytic results for Einstein solitons
• Gradient Estimates on Warped Product Gradient Almost Ricci Solitons
• Characteristics of conformal Ricci soliton on warped product spaces
• Eigenvalue estimates for a class of elliptic differential operators in divergence form
• On the construction of complete expanding gradient Rici solitons
• Properties of Complete Noncompact Warped Product Gradient Yamabe Solitons