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Remark about scalar curvature and Riemannian submersions

2005/04/20 by John Lott, Lott, John
Mathematics · #Bounded function #Curvature #Curvature of Riemannian manifolds #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Point processes and geometric inequalities #Prescribed scalar curvature problem #Ricci curvature #Riemannian submersion #Scalar curvature #Sectional curvature #math.DG

paper · pdf · doi:10.48550/arxiv.math/0504421

final version

openalex publication_date 2005/04/20 · arxiv created 2006/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space and fibers. We give an application concerning the scalar curvature of a smooth limit space arising in a bounded curvature collapse.

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