Holonomy of Manifolds with Density

2020/09/18 by Dmytro Yeroshkin, Yeroshkin, Dmytro · 1 citation
Mathematics · Physics and Astronomy · #53C25 #53C29 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2009.08733

openalex publication_date 2020/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss some examples and general properties of holonomy groups of ∇^φ introduced by Wylie and the author, the connection corresponding to the N=1 Bakry-Émery Ricci curvature, and also Wylie's sec_f. In particular we classify all possible holonomy groups in dimension 2 and also provide two infinite families: SL_n(ℝ) and SO⁺(p,q).

Citations

• On the geometry of Riemannian manifolds with density

Cited by

• Choi-Wang inequality for affine connections

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