Holonomy of Manifolds with Density

Abstract

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

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