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On the Prescribed Ricci Curvature of Noncompact Homogeneous Spaces with Two Isotropy Summands

Dustin Gaskins

Abstract

This work studies simply connected, noncompact $G/H$ in which $G$ is semi-simple, $H$ is connected, and $G/H$ has two irreducible summands. Here, we classify all such spaces and we provide solutions to the so-called Prescribed Ricci Curvature problem for all such spaces.

On the Prescribed Ricci Curvature of Noncompact Homogeneous Spaces with Two Isotropy Summands

Abstract

This work studies simply connected, noncompact in which is semi-simple, is connected, and has two irreducible summands. Here, we classify all such spaces and we provide solutions to the so-called Prescribed Ricci Curvature problem for all such spaces.

Paper Structure

This paper contains 6 sections, 23 theorems, 112 equations, 4 tables.

Table of Contents

  1. 1. Introduction
  2. 2. Preliminaries
  3. 3. Classification
  4. 4. Prescribed Ricci Curvature
  5. 5. $SO_0(1,7)/G_2$
  6. Appendix A

Key Result

Theorem 1

Let $G/H$ be simply connected with $G$ a connected semi-simple Lie group with no compact factors and $H \subset G$, a compact, connected subgroup. If $G/H$ has exactly two irreducible representations then $G/H$ is described by one of the following:

Theorems & Definitions (43)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • Remark 5
  • Remark 6
  • Lemma 7
  • Theorem 8
  • Remark 9
  • Remark 10
  • ...and 33 more