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The holonomy group of a locally symmetric space

Antonio J. Di Scala

Abstract

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.

The holonomy group of a locally symmetric space

Abstract

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.
Paper Structure (5 sections, 2 theorems, 6 equations)

This paper contains 5 sections, 2 theorems, 6 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic facts
  4. Local de Rham decomposition
  5. Proof of Theorem \ref{['main']}

Key Result

Theorem A

Let $(M^n,g)$ be a connected Riemannian locally symmetric space, not necessarily complete, without local de Rham flat factor. Let $\mathrm{H}$ be its holonomy group and let $\mathrm{N}_{\mathrm{O}(n)}(\mathrm{H})$ be its normalizer inside the orthogonal group $\mathrm{O}(n)$. Then $\mathrm{H}$ and $

Theorems & Definitions (2)

  • Theorem A
  • Theorem 2.1