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arXiv · 2009.08733

Holonomy of Manifolds with Density

Dmytro Yeroshkin
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Abstract

In this paper we discuss some examples and general properties of holonomy groups of $\nabla^\varphi$ introduced by Wylie and the author, the connection corresponding to the $N=1$ Bakry-\'Emery Ricci curvature, and also Wylie's $\bar{\mathrm{sec}}_f$. In particular we classify all possible holonomy groups in dimension 2 and also provide two infinite families: $SL_n(\mathbb{R})$ and $SO^+(p,q)$.

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Dmytro Yeroshkin. 2020-09-18. Holonomy of Manifolds with Density. https://arxiv.org/abs/2009.08733

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