Remark about scalar curvature and Riemannian submersions

Details Remark about scalar curvature and Riemannian submersions Remark about scalar curvature and Riemannian submersions

2005-04-20

arxiv.org/abs/math/0504421v2

Mathematics

Differential Geometry

final version

Scientific paper

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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