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Warped products and synthetic lower curvature bounds: an overview
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This is a survey about the contruction of warped products between (semi-)Riemannian manifolds and metric (measure) spaces. The resulting spaces will be semi-Riemannian manifolds, metric (measure) spaces or Lorentzian metric and metric measure spaces. We present details of the contruction in each case and we will highlight important properties like fiber independence and the energy equation. Warped products behave nicely in relation with curvature lower bounds. Here we will focus on sectional and Ricci curvature lower bounds and their Lorentzian counterparts. Throughout the article we provide many examples and formulate questions and conjectures.
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Warped products over one-dimensional base spaces and the RCD condition
An N-warped product over a one-dimensional base satisfies the RCD(KN,N+1) curvature condition exactly when the warping function is K-concave, obeys a boundary condition, and the fiber satisfies a related RCD condition.
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