Aloff-Wallach Spaces: Volumes, Curvatures, Injectivity Radii

Mikhail Alyurov

Aloff-Wallach Spaces: Volumes, Curvatures, Injectivity Radii

Differential Geometry 2007-05-23 v1

Authors: Mikhail Alyurov

Abstract

In this paper, we obtain two-sided bounds for the volumes of the Aloff-Wallach spaces $W(p,q),$ compute maximal and minimal sectional curvature for the spaces $W(n,n+1),$ and use this information to estimate the injectivity radii: We derive an upper bound for the injectivity radii of $W(p,q)$ and a lower bound for the injectivity radii of $W(n,n+1).$

Keywords

aloff-wallach spaces volume bounds sectional curvature injectivity radius riemannian geometry

Cite

@article{arxiv.math/0511620,
  title  = {Aloff-Wallach Spaces: Volumes, Curvatures, Injectivity Radii},
  author = {Mikhail Alyurov},
  journal= {arXiv preprint arXiv:math/0511620},
  year   = {2007}
}

Comments

21 pages, 2 figures

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