Some Geometric Properties of the Bakry-Emery-Ricci Tensor
Differential Geometry
2007-05-23 v2
Abstract
The Bakry-Emery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the Bakry-Emery tensor. We show that the Bakry-Emery tensor is nondecreasing under a Riemannian submersion whose fiber transport preserves measures up to constants. We give some relations between the Bakry-Emery tensor and measured Gromov-Hausdorff limits.
Keywords
Cite
@article{arxiv.math/0211065,
title = {Some Geometric Properties of the Bakry-Emery-Ricci Tensor},
author = {John Lott},
journal= {arXiv preprint arXiv:math/0211065},
year = {2007}
}
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final version