标题： 扭曲乘积和合成下界曲率：概述 显示英文标题

标题： Warped products and synthetic lower curvature bounds: an overview

摘要： 这是一篇关于半（伪）黎曼流形与度量（测度）空间之间扭曲乘积构造的综述。 所得的空间将是半（伪）黎曼流形、度量（测度）空间或洛伦兹度量和度量测度空间。 我们将在每种情况下详细描述构造，并强调纤维独立性和能量方程等重要性质。 扭曲乘积在与曲率下界的关系中表现良好。 本文将重点讨论截面曲率和里奇曲率下界及其洛伦兹对应情况。 在整篇文章中，我们提供了许多例子并提出了问题和猜想。 显示英文摘要

摘要： 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.