Some geometric properties of the Bakry-�mery-Ricci tensor

John Lott

Type: Article

Publication Date: 2003-12-31

Citations: 315

DOI: https://doi.org/10.1007/s00014-003-0775-8

Abstract

The Bakry-Émery 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-Émery tensor. We show that the Bakry-Émery tensor is nondecreasing under a Riemannian submersion whose fiber transport preserves measures up to constants. We give some relations between the Bakry-Émery tensor and measured Gromov-Hausdorff limits.

Locations

Commentarii Mathematici Helvetici - View - PDF
Deep Blue (University of Michigan) - View - PDF

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