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.
A general splitting principle on RCD spaces and applications to spaces with positive spectrum
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In this paper we develop a general `analytic' splitting principle for RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about RCD spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.
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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.