English

Einstein Constants and Smooth Topology

Differential Geometry 2025-04-01 v2 Algebraic Geometry Geometric Topology

Abstract

It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After reviewing subsequent progress that has been made on this topic, we then prove various related results, with the ultimate goal of stimulating further research on associated questions.

Keywords

Cite

@article{arxiv.2502.10560,
  title  = {Einstein Constants and Smooth Topology},
  author = {Claude LeBrun},
  journal= {arXiv preprint arXiv:2502.10560},
  year   = {2025}
}

Comments

21 pages, LaTeX2e. Revised version corrects various typos, and adds a dedication

R2 v1 2026-06-28T21:45:03.715Z